Avoiding double-count of cells with similar text

Hello,

I am faced with quite sticky a situation.

I have a huge table listing entries of sales throughout the year. Names of customers are in one cell (A). Because they were inserted manually, the same accounts were writted differently at different times. Ex: "CompanyA Ltd" or "Company A Ltd" or "Company A Ltd." or "Company A," etc...

The issue:
I want to count how many customers we have but want to avoid double-counting.

Step taken:
I have tried adding a helper column with the formula: if(sumif(A$2:A2;A2)=1;1;0) and summing the results of that column. Of course, this would be a good strategy to rule out exact matches. However, I have similar matches that I would like to rule out when counting.

Request:
If there is a function that accounts for similar text within a certain cell so that I could rule out similar matches, not only exact ones.

Attached is a demo file with the issue.

Many thanks!