In theory. In practice, probably not. Windows has a habit of leaving little droplets of history all over that come back to bite.
Best to just wipe and reinstall.
Windows itself? Not really. Third party applications that hard code the path? More likely.
Windows itself leaves the c:\users\<username> path as it was first set, even if you rename the username.
I can confirm this. Recently renamed a user as I handed off an old PC to my wife. The old directory is still there but now all the files within it are inaccessible. Caused a lot of issues!
This shouldn't happen. The directory is still there, but it also should still be your profile directory. Changing a user name shouldn't change the SID and make your files inaccessible.
Lots of things with Windows should not happen, but they do. It shouldn't forget that I have bluetooth hardware installed, but it does. Windows just (in)conveniently forgets things. Or, conversely, remembers things that should be forgotten.
A lot of weird things happen when you violate Windows' core assumptions about the file system.
Not really. Renaming the username-part of the user's home folder has all kinds of data loss potential (apps not being able to find documents, documents linked to each other etc.). Therefore Windows takes the perfectly appropriate approach of leaving the user's files named as they were. Permissions etc. all remain unchanged and allow the same renamed user access. Just the folder on disk shows the old name.
I just renamed my user, too, but I kept the same directory. No issues for the past month or so.
It's a rare operation that most people don't ever do, and so receives little testing. Certainly little testing in a real, deployed, messy system, and not just a pristine, vanilla QA image in some Microsoft Windows test bed.