First off, keep in mind that no matter what technique you use, it's going to be time consuming. Even carving your name into a nice soft tree would take time, if you wanted to do it right.
That said, this kind of thing is far easier today than it was years ago, thanks to a wide variety of modern and inexpensive diamond tools.
You can get a 4" diamond tile saw, and put it in a good 4" handheld grinder, to rough out the letters. Wash the rock off thoroughly, let it dry, and then draw the letters on it in something like Sharpie or other waterproof black marker.
Use the tile saw to hog out the bulk of the letters, but don't go too deep. Shoot for making a shallow "V" shaped groove. The ends will be rounded, but that's okay.
Next, trim up the ends- or even add serifs - with smaller diamond tips and wheels in a Dremel. The big wheel will have done the bulk of the work, so you'll just need to square up corners and whatnot.
All this while, by the way, have a garden hose keeping a trickle of water going on the work face. You don't need a gusher, just a trickle is fine. It both keeps the dust down and the abrasives cool. Watch out for water getting into the cutter motors- there are waterproof 4" grinders meant for tile saws, but I'm not sure about Dremels.
Hopefully your name is Jones or Smith, and not Trzetrzelewska or Wolfeschlegelsteinhausenbergerdorff or something.