That utility-shaped handle plus copper rivets was around for 1900 + and - ... I think you'd see some in some of the catalogues down the unfashionable end of the proceedings

I haven't looked into the name much ... but "F" can sometimes be "B" or "R" ...

I think you stopped at a pretty good time as far as revealing the stamp vs wearing it away.
Some WD40 and 2000 grit auto-paper and a light directed on the area might let you carefully take it a bit further.
Taking photos as you go is a good idea, because if you push it a little far and start to lose some details, you still have the pics from before.

Cheers,
Paul