How to make the names stored in a list unique?

I created a variable that will prompt users to input their names 20x, the all those names will be appended into an empty list that I created, but I need a function that will constant check each name that was entered and compare it to other names in the list in order to ensure that it is unique, if similarity is found, the function should automatically add a unique number to that name to make it unique. The function should also enable users to enter not more than 20 characters and not less than 3 characters for their names. Id really appreciate it if someone can help me with this problem, thanks in advance. Also I would like it to be done with python programming language.

Here is an example of how i have tried to make the validation

CLICK THE LINK TO SEE MY EXAMPLE

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