masc. proper name, a familiar abbreviation of Gilbert. As a typical name for a cat from c. 1400; hence gib-cat "a cat" (1590s), especially an old, castrated male, but also used as a term of reproach to an old woman.
1560s, type of iron hook, of unknown origin. As a piece of wood or metal to hold something else in place, from 1795. There are other mechanical senses, but it is not clear how, or if, the all are related. Compare jib, gibbet.