How did the titmouse bird get its name? It's not even a rodent!

The name titmouse is attested from the 14th century, composed of the Old English name for the bird, mase (Proto-Germanic *maison, German Meise) and tit, denoting something small. The spelling was influenced by mouse in the 16th century.

https://en.wikipedia.org/wiki/Titmouse

titmouse
"small, active bird," c.1325, titmose, from tit (2) (expressing something small) + O.E. mase "titmouse," from P.Gmc. *maison (cf. Du. mees, Ger. meise), from adj. *maisa- "little, tiny." Spelling infl. 16c. by unrelated mouse.
tit (2)
1548, "any small animal or object" (as in compound forms such as titmouse, tomtit, etc.); also used of small horses. Similar words in related senses are found in Scand. (cf. Icel. tittr, Norw. tita "a little bird"), but the connection and origin are obscure; perhaps, as OED suggests, the word is merely suggestive of something small. Used figuratively of persons after 1734, but earlier for "a girl or young woman," usually in deprecatory sense of "a hussy, minx" (1599). Tit for tat (1556) is possibly an alteration of tip for tap "blow for blow," from tip (v.3) "tap" + tap "touch lightly."

http://www.etymonline.com/index.php?search=titmouse&searchmode=none

So it's not a rodent? The mongoose ain't got no feathers, the mandrill ain't a man (and don't bore holes), and you can't knock nails with a yellowhammer.... https://en.wikipedia.org/wiki/Yellowhammer