In the minds of the original movie's makers, Spielberg, Lucas, Bluth, and the writers, Littlefoot is Littlefoot's real name.
FOr the sake of the original characters, this is very true.
I just can't help but picture an adult longneck named Littlefoot, and snicker a bit

An interesting point though, is most other children in the series have reasonable adult names.
Here's a list of young characters' names that seem most acceptable as adult names in my mind:
Cera - Nothing wrong with this as an adult name
Petrie - Sounds reasonable enough
Spike - why not?
Mo (I presume he isn't a grownup) - Fine name for an adult
Dana / Dinah - Reasonable names
Ali - Very reasonable
Hyp - Alright, not so bad
Nod - Possible
Mutt - Again, possible. This name wouldn't have the same connotations to dogs as it does nowadays.
A list of young characters' names that appear to possibly be unsuitable for an adult creature:
Tippy - hmmm...debateable
Ducky - Ok, a little cute but I can see it possibly existing at the time
Chomper - A little cutesy, but remember, the Gang named him when they were little kids.
Shorty - Ok, this may or may not, depending on how you view the name
Littlefoot - An adult apatosaurus named Littlefoot? I don't know... Interesting idea, but I just can't visualize this to be especially logical.
Skitter - Possible I suppose, but doesn't seem especially suitable in my opinion.
Some creatures seem to have names that fit them well into adulthood, yet some of them don't. There doesn't appear to be a trend for some species of dinosaur to use certain naming systems (Littlefoot, Shorty and Ali are all of the similar basic species). I wonder, why are some children named with full, Adult names, and some are named with more "childish nicknames" for lack of a better description?
My theory? It's simply based on the family's choice. Both methods are common, and no one thinks anything of it (except Cera when she teases Littlefoot in LBT 11, but this is an odd situation). Some families choose to give their children their full, adult name when they are born, and others may prefer to give the child a temporary nickname until either
1) The family gives them their adult name after a certain age
or
2) The child reaches an age where he or she may choose his own adult name.