Is it harmful to move someone with dementia?

We faced this with mom in the Spring. SIL called me one night and told me that mom's roommate, previously just cranky and sometimes loud, had gotten hold of a glass bottle and was using it to bang on her tray to get staff attention. Mom looked terrified. SIL wanted me to call and have mom moved.

I sent the NH administrator an email saying that mom was in a hostile and threatening environment that was clearly not good for her mental or physical health, and that I looked forward to talking with the facility at 10 to see what measures had been taken; and that if nothing had changed, I would be forced to take other actions.

Roommate was moved at 9:45 AM.

She's quite likely to turn up in her previous room on a regular basis, is the thing. I'm not sure I'd say harmful, though.

There is also the principle that if it's the roommate causing the problem then surely it's the roommate who should move?

Any relocation is hard on them. In your case, I imagine will be much easier. She is in the same place, same staff, same environment with staff that known her well. Setup her new room without her watching or participating. Make it look like her old room, it should be a relatively smooth transition. The staff know her well after three years and will know how to help her.