It’s definitely regional. For example I would only ever use ‘thing’ extensions, but like other people in the comments, other people only use ‘what’ extensions. Both will be understood though :)

It's regional and personal. I never use any "thing" extensions (I just say "the thing"), but I do use all the "what" extensions listed. I have a friend from my hometown who says "thingamajig" a lot. Not a lot of other people say it, but no one thinks it's weird when she does. So if there's one you like, go ahead and say it. People probably won't find any of them strange and will know what you mean, even if they don't say it a lot.

It might simply depend on which ones are used in someone's family or local area. I suppose 'thingy' is the most common.