Challenge to find unique matches without duplicates.

I'm running a matchmaking service where Participants get 1 unique match per week. I have a filtered list of names of people who are good matches. The challenge is such that:

Participants can only get 1 match; no duplicates. For example, Colleen Marks matches with Anh Vu. Therefore Anh Vu cannot match with Jorja Hester.

Must Maximize the number of unique matches based on this data.

I've attempted all kinds of sorting and replacement and cannot find an elegant solution to this problem. Hoping this community can help.

File is attached.
+-----------------+---------------------+
| Match 1 | Match 2 |
+-----------------+---------------------+
| Colleen Marks | Anh Vu |
+-----------------+---------------------+
| Colleen Marks | Arron Carrillo |
+-----------------+---------------------+
| Colleen Marks | Jason Shamil |
+-----------------+---------------------+
| Diogo Robins | Ben Katzenstein |
+-----------------+---------------------+
| Franco Wallis | Jemma Lennon |
+-----------------+---------------------+
| Franco Wallis | Alex Coisman |
+-----------------+---------------------+
| Franco Wallis | Julien Rowley |
+-----------------+---------------------+
| Franco Wallis | Eduardo Flores |
+-----------------+---------------------+
| Franco Wallis | Edwin Yung |
+-----------------+---------------------+
| Franco Wallis | Arron Carrillo |
+-----------------+---------------------+
| Franco Wallis | Jonathan Shan |
+-----------------+---------------------+
| Franco Wallis | Jose Siade |
+-----------------+---------------------+
| Franco Wallis | Juan C. Méndez |
+-----------------+---------------------+
| Franco Wallis | Kason Francis |
+-----------------+---------------------+
| Franco Wallis | Karam Werner |
+-----------------+---------------------+
| Franco Wallis | Liam Nguyen |
+-----------------+---------------------+
| Franco Wallis | Hadiya Dodson |
+-----------------+---------------------+
| Franco Wallis | Nico Kline |
+-----------------+---------------------+
| Franco Wallis | Paul Tu |
+-----------------+---------------------+
| Franco Wallis | Randolph Capocasale |
+-----------------+---------------------+
| Franco Wallis | Sadia Sharmin |
+-----------------+---------------------+
| Franco Wallis | Sara Huang |
+-----------------+---------------------+
| Franco Wallis | Rhona Kinney |
+-----------------+---------------------+
| Jorja Hester | Jemma Lennon |
+-----------------+---------------------+
| Jorja Hester | Alex Coisman |
+-----------------+---------------------+
| Jorja Hester | Anh Vu |
+-----------------+---------------------+
| Jorja Hester | Bala Venkatrao |
+-----------------+---------------------+
| Jorja Hester | Julien Rowley |
+-----------------+---------------------+
| Jorja Hester | Eduardo Flores |
+-----------------+---------------------+
| Jorja Hester | Erach Desai |
+-----------------+---------------------+
| Jorja Hester | Arron Carrillo |
+-----------------+---------------------+
| Jorja Hester | Jason Shamil |
+-----------------+---------------------+
| Jorja Hester | Jonathan Shan |
+-----------------+---------------------+
| Jorja Hester | Jose Siade |
+-----------------+---------------------+
| Jorja Hester | Juan C. Méndez |
+-----------------+---------------------+
| Jorja Hester | Liam Nguyen |
+-----------------+---------------------+
| Jorja Hester | Hadiya Dodson |
+-----------------+---------------------+
| Jorja Hester | Nico Kline |
+-----------------+---------------------+
| Jorja Hester | Paul Tu |
+-----------------+---------------------+
| Jorja Hester | Randolph Capocasale |
+-----------------+---------------------+
| Jorja Hester | Sadia Sharmin |
+-----------------+---------------------+
| Jorja Hester | Sara Huang |
+-----------------+---------------------+
| Jorja Hester | Imaan Joseph |
+-----------------+---------------------+
| Jorja Hester | Rhona Kinney |
+-----------------+---------------------+
| Karim Underwood | Baron Cao |
+-----------------+---------------------+
| Karim Underwood | Julien Rowley |
+-----------------+---------------------+
| Karim Underwood | Arron Carrillo |
+-----------------+---------------------+
| Karim Underwood | Herbert Rwamibazi |
+-----------------+---------------------+
| Karim Underwood | Jason Shamil |
+-----------------+---------------------+
| Karim Underwood | Karam Werner |
+-----------------+---------------------+
| Karim Underwood | Myoo Nadesan |
+-----------------+---------------------+
| Karim Underwood | Raymond Shih |
+-----------------+---------------------+
| Karim Underwood | Sam Horn |
+-----------------+---------------------+
| Karim Underwood | Imaan Joseph |
+-----------------+---------------------+
| Karim Underwood | Shiva Venkatraman |
+-----------------+---------------------+
| Misty Bell | Julien Rowley |
+-----------------+---------------------+
| Misty Bell | Eduardo Flores |
+-----------------+---------------------+
| Misty Bell | Erach Desai |
+-----------------+---------------------+
| Misty Bell | Jose Siade |
+-----------------+---------------------+
| Misty Bell | Juan C. Méndez |
+-----------------+---------------------+
| Misty Bell | Karam Werner |
+-----------------+---------------------+
| Misty Bell | Liam Nguyen |
+-----------------+---------------------+
| Misty Bell | Paul Tu |
+-----------------+---------------------+
| Misty Bell | Randolph Capocasale |
+-----------------+---------------------+
| Misty Bell | Sadia Sharmin |
+-----------------+---------------------+
| Misty Bell | Sara Huang |
+-----------------+---------------------+
| Misty Bell | Rhona Kinney |
+-----------------+---------------------+
| Momina Lara | Alex Coisman |
+-----------------+---------------------+
| Momina Lara | Bala Venkatrao |
+-----------------+---------------------+
| Momina Lara | Julien Rowley |
+-----------------+---------------------+
| Momina Lara | Eduardo Flores |
+-----------------+---------------------+
| Momina Lara | Erach Desai |
+-----------------+---------------------+
| Momina Lara | Jonathan Shan |
+-----------------+---------------------+
| Momina Lara | Jose Siade |
+-----------------+---------------------+
| Momina Lara | Juan C. Méndez |
+-----------------+---------------------+
| Momina Lara | Kason Francis |
+-----------------+---------------------+
| Momina Lara | Liam Nguyen |
+-----------------+---------------------+
| Momina Lara | Hadiya Dodson |
+-----------------+---------------------+
| Momina Lara | Nico Kline |
+-----------------+---------------------+
| Momina Lara | Paul Tu |
+-----------------+---------------------+
| Momina Lara | Randolph Capocasale |
+-----------------+---------------------+
| Momina Lara | Sadia Sharmin |
+-----------------+---------------------+
| Momina Lara | Sara Huang |
+-----------------+---------------------+
| Momina Lara | Skyla Newman |
+-----------------+---------------------+
| Momina Lara | Rhona Kinney |
+-----------------+---------------------+
| Monika Hopkins | Alex Coisman |
+-----------------+---------------------+
| Monika Hopkins | Bala Venkatrao |
+-----------------+---------------------+
| Monika Hopkins | Eduardo Flores |
+-----------------+---------------------+
| Monika Hopkins | Erach Desai |
+-----------------+---------------------+
| Monika Hopkins | Jonathan Shan |
+-----------------+---------------------+
| Monika Hopkins | Jose Siade |
+-----------------+---------------------+
| Monika Hopkins | Juan C. Méndez |
+-----------------+---------------------+
| Monika Hopkins | Karam Werner |
+-----------------+---------------------+
| Monika Hopkins | Liam Nguyen |
+-----------------+---------------------+
| Monika Hopkins | Hadiya Dodson |
+-----------------+---------------------+
| Monika Hopkins | Paul Tu |
+-----------------+---------------------+
| Monika Hopkins | Randolph Capocasale |
+-----------------+---------------------+
| Monika Hopkins | Sadia Sharmin |
+-----------------+---------------------+
| Monika Hopkins | Sara Huang |
+-----------------+---------------------+
| Monika Hopkins | Rhona Kinney |
+-----------------+---------------------+
| Rayyan Harvey | Alex Devereux |
+-----------------+---------------------+
| Rayyan Harvey | Bala Venkatrao |
+-----------------+---------------------+
| Rayyan Harvey | Ben Katzenstein |
+-----------------+---------------------+
| Rayyan Harvey | Cathy Keeler |
+-----------------+---------------------+
| Rayyan Harvey | Julien Rowley |
+-----------------+---------------------+
| Rayyan Harvey | Eduardo Flores |
+-----------------+---------------------+
| Rayyan Harvey | Erach Desai |
+-----------------+---------------------+
| Rayyan Harvey | Jonathan Shan |
+-----------------+---------------------+
| Rayyan Harvey | Jose Siade |
+-----------------+---------------------+
| Rayyan Harvey | Juan C. Méndez |
+-----------------+---------------------+
| Rayyan Harvey | Karam Werner |
+-----------------+---------------------+
| Rayyan Harvey | Liam Nguyen |
+-----------------+---------------------+
| Rayyan Harvey | Hadiya Dodson |
+-----------------+---------------------+
| Rayyan Harvey | Paul Tu |
+-----------------+---------------------+
| Rayyan Harvey | Randolph Capocasale |
+-----------------+---------------------+
| Rayyan Harvey | Russell Davis |
+-----------------+---------------------+
| Rayyan Harvey | Sadia Sharmin |
+-----------------+---------------------+
| Rayyan Harvey | Sara Huang |
+-----------------+---------------------+
| Rayyan Harvey | Rhona Kinney |
+-----------------+---------------------+
| Zeshan Lowry | Alex Coisman |
+-----------------+---------------------+
| Zeshan Lowry | Bala Venkatrao |
+-----------------+---------------------+
| Zeshan Lowry | Julien Rowley |
+-----------------+---------------------+
| Zeshan Lowry | Eduardo Flores |
+-----------------+---------------------+
| Zeshan Lowry | Jonathan Shan |
+-----------------+---------------------+
| Zeshan Lowry | Jose Siade |
+-----------------+---------------------+
| Zeshan Lowry | Juan C. Méndez |
+-----------------+---------------------+
| Zeshan Lowry | Karam Werner |
+-----------------+---------------------+
| Zeshan Lowry | Liam Nguyen |
+-----------------+---------------------+
| Zeshan Lowry | Paul Tu |
+-----------------+---------------------+
| Zeshan Lowry | Randolph Capocasale |
+-----------------+---------------------+
| Zeshan Lowry | Sadia Sharmin |
+-----------------+---------------------+
| Zeshan Lowry | Rhona Kinney |
+-----------------+---------------------+