When you said profile here, I take it that you meant Windows user profile, since I saw the question tag is for Windows 11 | Accounts, users and profiles.
If that's the case, a user profile by definition is the folder that hosts all of the data for that user that lives in C:\users.. Just want to make sure that's indeed what you want to remove.
If so, you cannot remove it while you are signing in with it. Instead, you need to log out of it, sign in with another user that has admin right.
Type sysdm.cpl in the search on the taskbar and hit enter, go to Advanced tab, click on the "Settings" button at the User Profile section. Then delete that user profile from there. Please leave defaut and public user profile alone and don't touch those.
Once deleted, type netplwiz in the search on the taskbar and hit enter, then you can delete the username for that profile from this page.
I hope that's what you were looking for.