In computing, is it correct to say "Username and password you have entered don't match"? Won't it sound like username and password should be the same?
The usage is correct.
"To match" doesn't always mean "to be identical." It can mean that a number of things go together, correspond, or form a set.
VERB: Correspond or cause to correspond in some essential respect; make or be harmonious.
[with object] ‘I thought we'd have primrose walls to match the bath’
[no object] ‘the jacket and trousers do not match’
So just as a jacket can match trousers without the jacket actually being trousers, a password can match a user name if the hash of the entered password is the same as the hash stored for the user name. This doesn't require the password to be character-by-character identical to the user name, or even similar.