Does anyone talk to you / about you in a third person while you are right there?

[BeamMeUpp]

Admittedly, this comes from my MIL, who is generally a good person, but I have kept distance over years as it took a house move to create boundaries. She does this weird thing like observational commentary like “BeamMeUpp is wearing her pink dress today” or “BeamMeUpp has a new vase” or last week “BeamMeUpp is pegging her washing out” literally watching me do it. Am I supposed to reply? It’s very annoying.

I voted YANBU as it's annoying and weird. Someone I used to come into contact with through work used to greet me by saying And how is Judiezones today?
It's patronising.

Ask her if she’s talking to herself or an imaginary person, say you’ve noticed her doing it a lot lately, and gently suggest a dementia check at the doctors.

Say "That's right. BeamMeUpp is hanging out the washing! BMU is making tea! What is BMU doing now? That's right. MIL is on fire! BMU is plumping cushions."

Look at her expectantly whenever you do something and indicate that you want a commentary.