Green’s Dictionary of Slang

a cat, thus used as a feline name.

1796		Grose Classical Dict. of the Vulgar Tongue (3rd edn).
1811		Lex. Balatronicum.
1823		Hants. Chron. 9 June 2: Sonnet to a Kitten. I’d rather see my Tibby frisk and play [etc.].
1859		Matsell Vocabulum.
1895		Crowe Aus. Sl. Dict. 85: Tibby, a cat.
1937		Eve. Standard (London) 11 Sept. 7/3: Oh, the mice are at it! I think we want Tibby here.
1947		Dundee Courier 28 Feb. 3/3: Tibby, a Persian cat [...] was missing for 13 days.
1956		Aberdeen Eve. Exp. 24 Nov. 11/3: [headline] Tibby Mourns her Late Master.