PS3 naming chests:

[ZSSD_founder]

As of version 1.13 PS3 console edition, you are now able to name chests. however there are a few bugs/oversights
You can only name a chest when you are not playing online (not a big deal)
naming a safe appears to cause the game to crash
if you play online you don't see the chests name when highlighting the chest or while your looking in it.

 

[Jasjenl]

Not being able to see the names online is by design, same as for not being able to see signs online: it would violate guidelines. The crash is something else though...