There are many kinds of India-inks and specialized writing fluids that will mark on metal and remain permanent. There are some fine-pointed Sharpie-type markers that will work. For information on theses inks and other methods click on this link:
https://www.durable-tech.com/marking/industrial-inksMy policy for signing prints is as follows:
On fine portrait prints, "fine-art" landscape and personal work, I hand sigh in ink. his is not distracting or deface the workin that I keep the signature smaller enough in part f the composition where it does not interfere. Painters and other artists routinely sign the work and it is considered in good taste.
In certain kinds of commercial work, I might include a watermark to signify copyright protection or to avoid unauthorized use or reproduction. Again, the signature is small but legible and in an area that does not affect the integrity of the work.
In other kinds of commercial and industrial work, especially for advertising and reproduction in printed material, displays, billboards, etc., there is no signature or watermark. Copyright issues are covered by contracts and arrangements with the clients and their agencies.
Occasionally, I may have a high volume portrait job such as photographing an entire graduating class of college or university faculty. For product purposes, I may goto gold foil heat stamping for the hundreds of points being made. Again, the replicated signature is kept small in proportion to the print size and placed in the area of the image where it is not overly conspicuous.
The heat-activated gold or coloured foil may be used to sign a metal print using a special pencil-iron.
Price delivered in albums are no usually signed but the signature is engaged on the inside cover or in a wedding album, I might hand sign the first or last print.
I have been dog this for many years. No client has ever complained and in fact, a few of them returned to have me sign prints that I may have forgotten to sign before framing or mounting.
Your signature shows your pride in your art. It is your "trademark" If it is tastefully done and applied it does not appear as blatant or tasteless advertising but it's good public relations, especially if you are building or sustain your public image.
I never stamp, sign, or write anythg on the back of a print for permanent keeping or display for fear it will seep through the paper or put an unwanted impression on the face of the print. I might label the back of a picture frame or other display method or mount but that is not a signature- it is lost if the prints are removed, remounted or reframed.