If you’ve got good control with your flexshaft, you could use a tiny
ball bur to carve out a signature.
If you’ve got a lot of time to learn a new skill, being able to
engrave by hand is a fantastic resource, and the tools required are
not terribly expensive. Beyond just putting your name on places,
learning how to use a graver will help with stone setting as well.
There are also machines that will engrave jewelery by tracing brass
copy type. They’re expensive, and can be a little bit fussy if you
need to put a signature in an odd place, but they make clean lines
and perfectly identical letters which can be scaled to many