My wife thinks there is two of me. What do I tell her?

Finally, someone is telling the truth about caregiving taking two.

At least two!

OP, Capgras Syndrome is the name in case it’s helpful.

Go along with it. If she says the other guy needs to come over, tell her you hope so too. If she says you're not her favorite, tell her sometimes you don't like yourself much either. Or don't say anything at all! Give her that devilish look and grin as you go to see what the other guy has cooked for dinner.

If wife wants something that you don't want to do, like taking her outside, tell her the other guy will do it when he gets there. Hopefully, she'll forget. Have fun with it. Maybe the other guy will start doing some of the grunt work of caregiving, like pushing her wheelchair.

I'm very curious about how this symptom developed. Can you tell us how you noticed it and if something precipitated it, like a stroke?

You can tell her anything that won't upset her; the goal is to keep her calm and peaceful. Does she think you have a twin? Or have a carbon copy of yourself ? (ooo, I just dated myself with that reference...)

It doesn't really matter what you tell her, as with her dementia she won't be able to understand or to retain your explanations. Watch Teepa Snow videos online; they will teach you a lot about speaking to the mind in dementia.