I just finished building a patio table that has a satin spar varnish finish. It turned out well but now my wife is asking if there is a way for my boys to permanently write their names or initials on it. My first thought was woodburning but I am not sure that would work because of the varnish.
Nail polish. Waterproof, durable, comes in a wide variety of colors, and it already includes a small brush.
A Sharpie will last a long time. If you want it really permanent, have them write in Sharpie or even a dry erase marker, which would allow revision if they mess up. Then go over it with a Dremel or engraving tool to carve it into the surface. It doesn't need to go very deep. You can then enhance it if you want by filling it with a dark filler stick.