Occasionally I get introduce by people using my former name & the gender they knew me as. I swear almost nothing is more awkward 
Correct them. Some folk need time to adjust. If they don't adjust, you don't need them in your life... 
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maybe, I've already done that privately to them, but do I wait for them to correct in intro, or should I just reply correcting?
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Haven't a clue to be honest... correct anyway. I get corrected regularly on many fronts, learn new things not obvious to me!
End of conversation
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