Here's what matters: sets only store unique elements. When you insert a duplicate, the set ignores it. This property solves the problem directly. Loop through the username and insert each character into a set.
I'll show you why this works. If the username is "abbac", you insert 'a', then 'b', then another 'b' (ignored), then another 'a' (ignored), then 'c'. The set ends up with three elements: 'a', 'b', 'c'.
After processing all characters, check the set's size. Odd size means IGNORE HIM, even size means CHAT WITH HER. The set does the hard work of tracking uniqueness for you.