On the occasions that I signed turned pieces - some were too small - I always used a fine indelible marker pen with my normal handwriting and usually the date. This way, as I saw it, each was individual.
I do also (did for a time making a living at it) make one-off pieces, basically what the client wants. Normally this is furniture, though I did occasionally make replica pieces for a builder who did period renovations. In the main it was doors and the occasional newel post or bits of stairs.
Call it a streak if vanity, but again I usually mark this furniture with a small named medallion about 38 mm diameter, that can be recessed somewhere out of sight. I obtained these from someone on this forum about 15 years ago and I'm coming to the end of my supply. These are pinned on. I think that he's moved on..... had a reputation for being a bit unreliable with deliveries, as I recall though I never had a problem in that area. Some older members may remember the guy........
I also put a coin with the year's date somewhere inside the piece. It will usually only be found if the thing is destroyed.
Anyway, in bigger pieces I may also secrete a note.... an idea I got from an old-school electrician I worked with as an apprentice who always stuffed his 'Daily Mirror', complete with all his jottings and half-done crossword under a floor board or down a wall-cavity.