Yes, it's possible to change your name a lot by creating and syncing accounts across the network. According to Name Change Limiting can be Broken, this is status-bydesign.
Impersonating others is a different issue. I think Brad Larson gives a great explanation:
Copying another Stack Exchange user's name and avatar is generally considered an attempt at impersonation, and will typically be rolled back by moderators. Filling out your profile to match the other person is certainly an attempt at impersonation, and will almost always trigger a profile rollback and stern warning.
Of course, this goes against the ToS:
Under no circumstances will Subscriber use the Network or the Service to (a) send unsolicited e-mails, bulk mail, spam or other materials to users of the Network or any other individual, (b) harass, threaten, stalk or abuse any person or party, including other users of the Network, (c) create a false identity or to impersonate another person, or (d) knowingly post any false, inaccurate or incomplete material.
The key part is (c):
Under no circumstances will [the] Subscriber... (c) create a false identity or... impersonate another person
If you see someone trying to impersonate another user, you should flag for a moderator and explain this. (You get bonus points if the user was trying to impersonate a mod and that mod handles the flag