Beth

Beth is the second letter of the Hebrew alphabet, and means either "house" or "daughter". It is a MUCH older name than Elizabeth. It is not just a nickname.

The name Beth is a nickname for many many other first names, so unlike what one has said here it does not mean "house of God", nor does it mean "house." The name Beth doesn't mean anything.

Beth has no meaning by itself, since it is a nickname. Even used as a stand alone name it means nada.

Beth means "House of God".

Bethel means "house of God." Beth alone simply means "house."

It doesn't REALLY mean anything when it comes down to it---it's the name it derives from, such as Elizabeth, that has the meaning (and the form Beth, as a given name, still lacks a real meaning because it's derived from one of those names).