Challenge to find unique matches without duplicates.

The problem is that I don't think going with matches from the top down will result in the maximum possible matches for everyone in the list. For example, if Franco Wallis seems like a popular person so I should save him for later (because he's more flexible) and first match the hard to match people first? Does that make any sense.

And yes, looking for a formula that is repeatable for future data sets in the same 2 column format.