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I remember engraving my DL on several items, back then. I don't know how much you may want to invest in it, but I would suggest looking for an engraver, who could turn it into something decorative. Sort of like covering a bad tattoo. JMHO

Sand it off, polish it up a bit, add some cold blue. A Winchester Ranger is not a highly valuable firearm, so it shouldn't diminish the price much. If you aren't ever going to sell it don't worry about it.

got a relative?

If you plan to leave it to family when you die, leave it the way it is. If they deserve to inheirit a firearm, they won't mind.

If you want to sell it, gently mill out the area with your DL if you can do so without affecting the serial number. Inlay copper or some other "soft" metal. Decorate the inlay by etching or other appropriate method. Have the decoration done by an experienced (amatuer) metal worker if you don't feel confident in your ability.

Gunsmith can file it down.
Laser engraver may be able to cover it.
Someone could weld on to it and then grind it down and re-finish it.
Put it under a mill and cut it out, very carefully.


Lots of options....

Those don't go very deep and can be removed without much affect on the roll marks and stampings, or just leave it. I bought a Ruger Super Blackhawk cheap because somebody had written on it with one of those. Sanded and polished it out and then went over it with cold blue.

Jeff

And in the future (and for anyone else considering this), if you're resolved to do it, put it in a place that doesn't show, like under a handgrip or stock.

It didn't originally occur to me that your shotgun has an alloy receiver instead of steel (Correct?)
Removal of the engraving will be a little easier and you won't have to worry about polishing it to match. You can refinish with durocoat or something similar afterward.

In my opinion, leave the gun alone and keep it. Or give it to someone in your family that would use it. I would seriously leave it alone. Engraving a gun is like stippling a plastic pistol. Once you do it no matter how good it looks, unless the buyer specifically asks for it, you will always get less for it than a clean version. If you wanna give it away I’m sure I could help unload the burden

“I bought a Winchester Ranger in about 1980...but for whatever reason...I used one of those electric vibrating engravers to add my Texas DL”

I think some good folks in law enforcement were aggressively promoting the idea of engraving personal items in the early eighties. I was in the military then and clearly recall the MPs assisting me in the engraviing of both my TDL and SSN on the few valuable items I owned. To this day I have a vintage reel-to-reel tape recorder that I am reluctant to sell because my personal data is engraved into an otherwise pristine unit.