Firstly is it possible that a single user uses different registered user names. Secondly is it possible that he votes to close a thread with his different user names? I hope not.
Yes. It's possible.
People can open more than one account, and some people do. If both accounts have reached 3,000 points then both can vote to close.
The SE software does its best to disallow a user to abuse the system in the form of two accounts acting simultaneously towards the same goal. If a user has voted twice to close a question, or voted twice for, or against, a post -- that's an abuse of the privilege given to the user (that is, using the site in the first place), and if caught such user is usually subjected to suspension, and/or account deletion.
Note, however, despite the fact that SE guards its methods of finding such abuse secretly, there are probably people who managed to infiltrate through it and have gamed the system in one way or another. Keep in mind, though that reaching 3,000 points is a long-term work; and the more you abuse the system there is a greater chance that you'll get caught.
I doubt that anyone have worked through all that trouble just so they can gain an extra close vote.
Yes, it is possible to have different registered accounts. There are perhaps a variety of reasons why you might do such a thing; the one that comes to my mind might be to have a throwaway account to ask lower level questions as an effort to save face (a smurf account). I don't encourage or practice this behavior, but I've seen it before.
In short, it is not prohibited for a single user to have multiple registered accounts.
However, users must not use multiple accounts to game the system, or to any benefit other than the extra anonymity. In particular, the user's accounts should not upvote/downvote any question/answer provided by each other, nor should any two upvote/downvote the same question/answer given by another user. You may also not use a sockpuppet to avoid main account suspension. A general bit of guidance would be for subaccounts to never interact with eachother, and only one should ever vote on anything else ever. And if you think something might not be legit, just don't do it.
There are SE scripts running to search and identify users who bend/break these rules. There are also scripts that automatically identify suspicious voting patterns that can, depending on the severity of suspicion, immediately and automagically invalidate the votes. Mods are also on the lookout, and we have periodically dealt with people attempting to use sockpuppets to their advantage.