People will think of it as a distinctly unusual way of speaking unless you specifically adhere to the "The name's Y, X Y" formula - and if you do that, people will almost universally think of it as a reference that's tired at best. My advice is to not try to be creative with stock phrases.
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huaracheIs it okay to say "what's the name?" to ask your name just to make it sound different than usual?You can say all sorts of things that sound different or unusual, but you have to be psychologically strong because people might think of you as foolish or silly when you
... is it okay to start your answer with "the name is..." instead of "my name is"