So, I'm just about to finish my map (maybe one or two more things) but I came up with a last minute problem. Someone had told me that my map name was already taken. 

However I feel like putting my .map into the script placer and just generating it would leave out things I put into my gsc (like a zombie counter) and other things IDK about.

Any help would be appreciated 

As long as you don't have a custom menu or intro you don't have to worry about the actual map name.
CoD gets the name that is displayed in the mod-list from the folder your map is saved in (the one in the appdata).

You'll just have to rename that folder and everything should be fine.

I changed my mod name in the Appdata mods then I built my mod, but It just made a new folder... Also I do have a custom main menu, but all it is is really just Different text for the solo and coop button. 

Just rename it after your final compile:D
And if you use a custom menu you can normally choose which name is displayed.