You can use the short name if you want (as long as someone else hasn't registered it) simply by issuing /nick me1. Note that nicknames are global in IRC, though, so if you are in any other channels this will also change your nickname there. You can just use /nick longname16 to go back to your registered name, although depending on how FreeNode's services are configured, you may need to /msg nickserv identify <password> again. Note that if the short nick you want to use is already registered by someone else, you won't be able to use it. But unregistered nicks are fair game for anyone that wants to use them.
Basically, the thing to understand, is that registered nicks in IRC are not like an account on a website - you don't need to "sign in" to a nick. Anyone chooses whatever nick they want, and you don't have a specific nick that belongs to you, you can use whatever you want (as long as someone else currently in the server isn't using it, since nicks need to be unique at any given time). Thing is, most people will choose the same nick over and over (so that everyone else will know who they are), and it's annoying if you join the server and someone's using the nick that you always use. So many IRC servers provide nick registration as a convenience, so that if you always use the same nick and you don't want someone else to use it, you can set a password on it to make sure it's always available for you and no one else can use it to pretend to be you. It's not something you have to do in order to "log in" to the IRC server.
On the other hand, note that there are some channels that require you to have registered your nick in order to join. This is just a simple method to avoid trolls, since the extra command it takes to register a nick will deter a surprising number of people. These aren't very common, though.