If you rename a profile, the old one continues to exist as well.
It will only be shown after you restart Konsole though.

Reproducible: Always

Steps to Reproduce:
1. Create a new profile, let's say "test"
2. Edit the "test" profile and change the name to "test2"
3. Close Konsole and start it again

Actual Results:  
"Manage Profiles" now shows a "test" and a "test2" profile.

Expected Results:  
"test" should not be there any more, only "test2.

The old profile is never deleted from ~/.local/share/, it just isn't shown any more after renaming until you close Konsole.

This happens with Konsole 15.12.1 (KF 5.18.0, Qt 5.5.1).