A hallmark proper is a mark to show the proof of precious metal. It can only be applied (in the UK) at one of (I think it is still) four testing stations. It shows what the metal is, what proof, and what year it was sent for assay. Items which do not come up to proof are smashed so they cannot be sold. The marks are punched into the metal with an engraved punch and a hammer, not engraved or cast or etched. Punched. Metal punch, hammer, thump. (Indeed you sometimes have to re polish the item because there is a dent on the underside!)
In addition a maker may have his own mark affixed to a work to claim and identify it. I have a mark, which is my initials in an egyptian shaped cartouche. That mark has never been issued before and never will be to anyone else. I went to Goldsmith's Hall in London and we looked through the original records to see whether my initials in that particular shape had been issued. It was an amazing experience. Now I don't do much silversmithing (time!)
If anyone is interested in learning more there is much information on this website
http://www.thegoldsmiths.co.uk/
The Worshipful Co of Goldsmiths is one of the twelve original livery companies of the City of London.
I suspect that what you are calling a hallmark (mark made in an assaying hall) is in fact a manufacturer's mark (which is why it varies without records being kept)
I cannot change my mark.