Can you make 3D Studio Max 8 warn you when you dettach a part of a mesh and type in a name that already exists? It just renames it instead. Not that I can't be bothered renaming (again) the renamed extirpated pieces, but it would speed up things a lot for me.

At present I don't know of a way of doing this other than writing a custom Max Script. Another option is to copy and paste the name and manually incriment the number, but this isn't much more efficient than what you're probably already doing.

No, there is no way. Besides, I don't see what the point of having an object of the same name be in your project. That just simply doesn't make sense. It doesn't in programming either... in all languages I know you can't have a variable of the same name as a different type. Pretty similar concept here. The overall answer again is now. I don't personally even bother with names, it's a waste of time to me unless you have hundreds or thousands of objects in the scene.

I don't want to have multiple objects with the same name, it's just that when renaming them I might call one Door 8, and the next one Table 0, 1, 2...30 and when I'm going to name another door I don't remember if the last one was 7 or 6 or 9 or 8 and so I might name it Door 8 and max won't even tell me there was a Door 8 already.

By the way, I have to do that because my game engine expects some objects to be named in certain way, so I have to name all rooms "Room {number}" and all doors "Door {number_of_room_A} {number_of_room_B}".

What I'd suggest would be a combination of naming each object just 'table' or 'door' without any numbers, then writing a quick script to scan over the scene and automatically number things for you once you're ready to export.