If you are prompted for another user's password when you logon, chances are that the profile used to create your account had a persistent connection. Before copying a profile, an Administrator should edit:

HKEY_USERS\<SID>\Network\<Drive Letter>

They should double click on Username and empty this REG_SZ value by removing the <Domainname>\<User> string.

NOTE: Do NOT delete the value, just the string data.