tallyho
What I would do is find someone with one of those plastic strip label makers. Print your name on a black strip and stick over the engraving.
It would look ok, and for some one inquisitive, you just tell them you labeled the gun so it would not get mixed up.
This would be an easy fix and only you would know whats under the label.
I bought a Browning Midas Grade O/U trap gun it had the previous owner name in gold in three different places. I send it to an engraver who made gold inlays where the names were and engraved over another. I could afford to do this because I bought the gun for a song because of the engraved names.
Your gun could be done the same way by milling out a small panel and fill it with a thin silver or gold strip. Polishing the numbers of would create an uneven surface. The whole flat surface would have to be milled or ground off with a surface grinder , polished and reblued.