The point is we need to the name the things correctly. In case of a fork we have two coins and every users and every service has to be able to distinguish between them. This has to be done until one of the two chains is not used anymore.
It makes no sense to rename the longest Bitcoin chain as this the original chain with the original consensus rules. As BitcoinXT is the new coin we have to find a new name for this coin which could be BXT.
Indeed that is the point. The way the fork is programmed, every transactions will be in principle valid under both sets of 'consensus rules' and executed in both branches of the blockchain. Sometimes, by accident or crafty art, a transaction may be executed in only one branch; or the same input may be sent to two different adrresses, one in each branch. However, ordinary clients will have no control over such events (and may be confused by them).
So, it does not make sense to call either branch an altcoin, or to invent a symbol for it. Splits of the chain (ophaning) happens all the time even when everyone is running the same version of the software.
It is also not logical to say that one branch is an altcoin because it uses different 'consensus rules' than those that were in force before. Once a block smaller than 1 MB has been solved, it is impossible to tell which software was used to solve it. (There is a version field in the header, but the software can set ti to anything it wants; it is ignored by the protocol.) Thus one can claim that the limit has always been 8 MB since genesis, or 17.3 GB; and both branches would then be valid according to these 'consensus rules' too.
Or also: suppose that someone posts a version of the software -- let's call it BitcoinZZ -- that does NOT cut the block reward in half when it should. If that version attracts enough miners, but not 100%, the chain will split into two branches, one with 25 coins of block rewards, as in the common trunk, and the other with 12.5 coins. Which one will be the true Bitcoin: the one with a change in the reward, or the one whithout the change?
This question is connected tp a famous logical/philosophical paradox of Bleen and Grue. Everybody knows that emeralds are grue, and sapphires are bleen. But a curious thing will happen on March 17, 2017, when emeralds will suddenly become bleen and sapphires will turn grue. Some weirdos say that things are 'green' if they are grue until that date and bleen afterwards; but why would one give a name for a color that becomes a different color at some date? That is stupid...