I renamed a box and the floating text for "name" didn't change. I did this more than once to make sure.
You can deselect the floating text then select it to show the new name.
Yes, I have experienced this as well, on all my boxes. Seems to be a glitch with the new floating text setup and the ability to choose which labels to display. The floating text does not automatically refresh when the name is changed, you have to deselect and reselect the "name" option from the menu. I don't know if this is a limitation within SL because floating text can be a pain or if its just something that needs to be fixed with the next update.
This happens sometimes with non KittyCats items that also use floating text. Its just something that hits more with lag. I have a status notifier phone that sometimes can take an hour to show me online, which is fine as I am a naughty kitty who likes to hide. The more lag in an area the longer the delay seems to be. I hope this helps.