You don't want to bury it, look for a reasonable cover.
Google "plumbing access panel" and you will find something that looks decent.

Is there some kind of ring I can put around the drywall opening to finish off the edge of the drywall?

So looking at this panel, for example, the flange fits around the opening and finishes everything off.

Jake, the plug sticks out of the drywall about an inch or more. The round part is more or less flush with the drywall, and the cube sticks out into the room at least an inch. It’s not perfectly aligned.

Repair or replace the drywall around the clean-out pipe and use a recessed plug.

http://www.real-titeplugs.com/real-tite-plugs-line.html

https://www.amazon.com/Sioux-Chief-Recessed-Plug-4/dp/B000JV9NQ2/ref=pd_sim_60_2?_encoding=UTF8&pd_rd_i=B000JV9NQ2&pd_rd_r=f42272a4-8e7b-11e8-8c43-8bf4bd0474d3&pd_rd_w=AOhwQ&pd_rd_wg=WUCku&pf_rd_i=desktop-dp-sims&pf_rd_m=ATVPDKIKX0DER&pf_rd_p=2610440344683357453&pf_rd_r=62A70YZSCY9P01HWGCVD&pf_rd_s=desktop-dp-sims&pf_rd_t=40701&psc=1&refRID=62A70YZSCY9P01HWGCVD

There are also cover plates available in chrome, etc. to cover the drain plug but you'll need to find a plug/ cover plate combo that are compatible. A PVC cover plate would be paintable.

Let it be. Paint it, with the rest of the wall. You won't see it, in a couple of weeks.

I chipped away at some of the texture and paint that had been covering it to expose the black part. Now I’m wondering if I’m seeing a pipe or fitting around the circumference of the actual plug that unscrews. If so, I should be able to drywall mud and caulk up to the edge of the black part, because that would stay stationary if the plug were to be removed. Is that correct?

This is what my wall looks like:

See the line that goes around the circumference about 1/8 inch in from the outside? Is that where the plug would separate from the housing (or whatever you call the surrounding piece)? If so, I could patch and caulk right up to the exterior of that if the plug could be removed from the inside of that piece (if it is a separate piece). The link I posted above makes me think I am looking at two pieces, one stationary and the other unscrewable.

Please let me know if I am getting this right and if it’s ok to patch and caulk up to that outside piece.

(Sorry to be so wordy.)

And yes, I would paint it after it’s all cleaned up.

And I like the idea of recessed, but I don’t want to hire a plumber to do that right now.

The article I linked above said this:

“You may see a 3-inch- or 4-inch-diameter pipe stub extending out from the slab floor. The stub out will have a screw-in plug, which is your main drain access.“

I assume this is what I have since it looks like their pic, so it should be ok to patch and caulk to the pipe stub. Mine is vertical in a wall, not horizontal in a floor.

Question: I was looking at clean out parts online, and I read that you don’t use primer with abs (the black ones), but you do use primer with pvc (the white ones). I assume they are not talking about paint primer? Do plumbers use a different primer? I don’t want to compromise the plastic when I paint! (My pipe and plug are black.)

And I like the idea of recessed, but I don’t want to hire a plumber to do that right now.

Jane, the plug is recessed. No need to hire a plumber. Just unscrew the old one and replace with a recessed plug with a compatible cover plate. Doing that will get rid of the square knob plug and the cover plate will hide the new plug.

I read that you don’t use primer with abs (the black ones), but you do use primer with pvc (the white ones).

That's a primer that is used to clean the plastic before the solvent weld glue is applied when making a fitting. Stuff a plumber uses. NOT paint primer.

I think you can get an acceptable repair on the drywall by coating the crumbles and paper with Gardz (let dry) and then filling with hot mud (Durabond, setting type drywall compound; the powdered stuff that you mix with water.)

As far as unscrewing it, I’m concerned that (1) I don’t know what is going to explode out of the pipe, (2) I don’t know if it will unscrew without falling apart, (3) I don’t know if it will unscrew at all, (4) I don’t know if I can get something to screw back in there. So I might leave that to a pro who opens it up when/if the need arises.

If a cover plate is still needed with a recessed plug, I think instead I’ll just clean up the drywall, paint, and be fine with it. It was the raw edge of the drywall that I was most concerned with. I can make that clean if the pipe surround does not need to be free.

Thanks everyone!

It is called a: cleanout.

There should be no pressure, it is higher than the waste, and it is connected to an air vent.

If you do not like the black cover, there are decorative replacements.

A few days of spackle work will fill in the cracked drywall. Replace the black cap with a decorative screw on or thread a replacement cap and use a cover with a screw.

you unscrew the cap, flip it over and reinstall it.

have a bucket and sponge if you are worried

about anything coming out.

best of luck

"I would suggest you to leave it like this!"

Jan Mackenzie, 2 1/2 years later for that tidbit?

Just flag the spam.