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I understood the OP's question to be about an unsolicited disclosure, and I can't really think of any circumstances under which that would be relevant/appropriate. In response to a direct question, I suppose it would depend on whether it's any of the student's business. Lying about it certainly doesn't seem appropriate.
... it really isn't relevant, except to explain to the students why I interrupt and correct him all the time
I DM for my husband. He introduces me as his wife. It isn't weird. But it really isn't relevant, except to explain to the students why I interrupt and correct him all the time
The direct question is the appropriate circumstance to me. Unsolicited not so much.
Badly worded poll IMO.