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What is appropriate size stamp ( small enough) to request when ordering a stamp to put name on bottom of stummel/ shank

The smaller the stamp, the easier it is to pull off a successful impression, particularly on a curved surface. There's a trade off, though. The smaller you go, the less room you have for design. It's worth having a conversation with whoever is making the stamp to see how they assess your design versus the size. There are limitations as well with what the stamp can do. My stamp is about 3/8x1/2" and it's a bit tricky to stamp. I'd say, try to keep it to a 3/8 circle or less, and the simpler the better...

Thank you. Good advice.

If you can keep the impression narrow/sharp, the stamping will last longer, Blunt impressions tend to dent the wood while narrow impressions actually cut wood fibers. Dented impressions will “steam out” with multiple smoking cycles, while cut impressions will last longer.
DocAitch