If you create a new item in the object list or a new cell does it cause any problems if you change your mind as to what you want the ID to be? Say if you want to change the name of a cell from myBasemant to MyStronghold or the name of a NPC? I've been calling items I create MyWhatever. I would like to give them a less generic prefix say my ititials and the initials of my mod. Is it too late? I don't mess with the vanilla items.

I have no reason to believe this will be a problem.

I've done it a few times myself in the CK with no adverse effects.

I have much more extensive experience with the construction set for oblivion and it never gave me a problem then (renamed things frequently).

*EDIT: The initials of your mod or name as a prefix is considered good practice as it reduces potential EditorID clashes of new references to an absolute minimum.

The CK seems good about reflecting updates to EditorIDs everywhere. The one case I can think of where that isn't a good idea is quests with voiced dialogue: because the voice files are named according to the quest, if you change the EditorID of the quest, you'd need to manually rename all its voice files.

I seem to be having trouble renaming one thing. I changed the ID of my cell OK but the option the change the Name is greyed out and everytime I type in a new name it just beeps at me. I've tried it with and without the cell being active. Any suggestions?

Click on another cell in the list and then back on the cell you want to change. That turns on the options in the dialogue.

That seems to happen if the cell you want to edit is the active cell. Feels like a fail safe to prevent unwanted edits.