What to do with wrong size hole after changing bathroom vent fan

You didn't mention what kind of ceiling material, which is the most important component of your question. I will assume it's drywall. Drywall is relatively easy to patch so no one will ever know it was different before. The exact nature of the repair depends on what you end up with after installing the new fan. You will end up painting the whole ceiling.

As for getting the old one out, you can always use brute force to bend it up until it yields. My question would be how you plan to install the new one if you have no access above. Since you have to patch anyway, maybe the best solution would be to cut out more of the drywall between the ceiling joists exposing half the width of the 2x joist so you have something to attach the new drywall to. You need to make a big enough hole so you can install the new fan. Make sure that the vent goes outside. Then it's mud, tape, and paint. Gosh that was easy.

https://www-familyhandyman-com.cdn.ampproject.org/c/s/www.familyhandyman.com/bathroom/exhaust-fan/how-to-install-a-quiet-bathroom-fan/amp/

http://www.ventcoversunlimited.com/custom-metal-registers-and-air-return-grilles/

http://www.creeklinehouse.com/2013/07/how-to-paint-your-vent-covers-instead.html

had a similar problem with a new ceiling fan.... a medallion took care of that problem...there are fancy ones and some that are less so....look at Lowes or other home stores....

Since popcorn has those little foam beads in it and is applied with a gun I would be interested in knowing how you would match it.

I have enough dislike of the stuff I'd probably get my scraper up there, pull the beads off, then start sanding. Hey, you gotta fix the big hole around the fan anyway.

As I reimagined my bathroom I ended up with three new switches and an outlet on the entry wall. Really busted up the drywall. The main patch was about 20" by 20" with a bunch of holes and notches for the electrical boxes. It turned out looking so good it is hard to believe that it was ever touched.

Ceilings are somewhat less fun but you have a more straightforward patch. I am a hack at all of this and if I can end up with a professional looking job, you can do this.

With replacing bathroom ceiling fans is it not so much that the new fan has a different sized cover (the part that shows when you look up at the ceiling) and therefore will need a different sized ceiling hole to get it to stay up.

The source of the main problem is often the size (circumference and length) of the inside vent.

When you are shopping for a replacement fan, make sure that you purchase one that is suitable for being retrofit into an opening that already has a fan installed.

Many fans for sale in retail outlets are suitable only for being installed into a space where there previously had not been any fan, thus a new installation.

Depending on brands and sizes of fans, there are also different styles of how the vent is mounted up into the ceiling. Before purchasing a replacement fan, take apart the old one to see how the vent and inside workings are mounted.

Re-read Ken's comments. He knows what he is talking about.

https://www.kulgrilles.com/collections/vent-covers-by-kul-grilles-modern-grilles-for-the-modern-home

Use a wide Plastic or timber trim to go all around it.

Search for goof plates. You can special order them in the size you need. They come in square and round.