In Japanese sword terminology; 'mei' is most commonly used to refer to a sword's signature. However, in Japanese craftsmanship it is more than common for a maker to sign their work. You can find 'mei' in woodworking, gun smithing, lacquer work, sword furniture and more!

When speaking of a Japanese sword with katana geometry and mounting one would say katana-mei and when the sword has a distinct tachi geometry one would use the term tachi-mei.
In general, the signature on a Japanese swords always placed on the omote side. A phenomenon that arises with katana- and tachi-mei is that the smith's signature will be on opposite sides of respectively a katana and tachi.

As omote means 'showing side', the signature will be visible from the side that faces away from the wielder. As the tachi is worn cutting edge down and the katana cutting edge up, automatically the omote side with be reversed and thus, also the signature will be on the reversed side.

Another interesting etymological point is that the term mei does not always have to mean a person's signature. The term indeed can be translated as a name (which is the case with signing a made object) but also imprint, texture or mark.
Whereas a signature as used in katana-mei would be written as 刀銘, a stone pattern would be written as 石目~ishi-mei and the marks of a file or rasp as ヤスリ目~yasuri-mei.

Interesting food for thought, can anybody guess what is the signed object in the picture? ;)