Program to automate clicking on the new button on a chat website until the username matches certain conditions
Your third part is wrong, I think.

nonCompatible = 'female' not in name


will only run against the value of name at the time of execution, so nonCompatible will end up either True or False, and won't change unless you reset it elsewhere in the while loop.  You may want to either inline it:

while 'female' not in name:
    ...


or abstract it:

def nonCompatible(nym):
    return 'female' not in nym


while nonCompatible(name):
    ...