In my opinion, it would still be called a Proof as that designation is based on how it is manufactured, not what the current condition is. If you submitted it for grading from one of the houses that do that (NGC, PCGS, etc) any wear or dings it has accumulated in the process would affect the current grade. It would likely be graded PR-55 or some such designation, where the PR indicates it was made as a proof and that the current grade is 55 or almost uncirculated or slightly used (to use chip terms). In my opinion, the grading house would use the PR to say it was made as a Proof (double struck or some such difference). The numbers that follow would indicate the amount of wear or number of marks that the coin has accumulated while in circulation.

I've never actually seen a slabbed and certified coin graded this way but in my opinion, PR-xx is a reasonable way to do it. I've seen quite a few coins in circulation that have a Proof appearance but also indication of wear and dings from the handling. I've often seen price-lists published by the grading firms that use grades like PR-66 or PR-68 to indicate the strike or the presence of marks have made this proof coin less than a PR-70 (a perfect proof). It makes a big difference in value of the coin.

If you should submit your 25c coin for grading, how about showing a picture of the holder on this bb so we can see how it's really done.