What does my-oh-my mean?

Yes, more or less. "Oh my!" is a euphemism for "Oh my God!", I believe.

I think you are using the word "mane" when you mean to type "name".

"My, oh, my" is an expression of surprise, but not necessarily joy. It's also used to express dismay at a situation.

(JOY) Martha saw how her nephew had grown. "My, oh, my!" she exclaimed,"You're a foot taller!"
(Dismay) Martha saw the mess in the living room. "My,oh,my!" she said to herself,"This is going to take some work."

O: I have no proof for this but I think My, oh, my is a variation of "Oh, my god!" which is also an expression of surprise. In these modern times "Oh, my god." has been changed to the very informal 'omigawd' or 'omigod' or the even shorter, used for messaging "OMG".

Joe(I have no knowledge of a Club called "My, Oh, My" but it sounds like fun to me.")Nation

Thank you both.

(PS Yes, mane is the typo of name)