fin (n.)

late Old English pinn "peg or bolt of wood or metal used to hold things in place or fasten them together," from Proto-Germanic *penn- "jutting point or peak" (source also of Old Saxon pin "peg," Old Norse pinni "peg, tack," Middle Dutch pin "pin, peg," Old High German pfinn, German Pinne "pin, tack") from Latin pinna "a feather, plume;" in plural "a wing;" also "fin, scoop of a water wheel;" also "a pinnacle; a promontory, cape; battlement" (as in Luke iv.9 in Vulgate) and so applied to "points" of various sorts, from PIE root *pet- "to rush, to fly."

De Vaan and Watkins say Latin pinna is a derivative of penna, literally "feather" (see pen (n.1)); older theories regarded pinna as a separate word from a root meaning "sharp point." The Latin word also was borrowed in Celtic: Irish pinne "a pin, peg, spigot;" Welsh pin "a pin, pen."

The transition from 'feather' to 'pin' (a slender or pointed instrument) appears to have been through 'pen,' a quill, to ' pen,' a style or stylus, hence any slender or pointed instrument [Century Dictionary]

As a part of a lock or latch, c. 1200; as a control for a mechanical device, late 14c. The modern slender wire pin, used as a fastener for clothing or in sewing, is attested by this name by late 14c., perhaps late 13c. Transferred sense of "leg" is recorded from 1520s and holds the older sense. The meaning "wooden stick or club set up to be knocked down in a game" (skittles, bowling, etc.) is by 1570s.

Pin-money "annual sum allotted to a woman for personal expenses on dress, etc." is attested from 1620s. Pins and needles "tingling sensation" is from 1810. The sound of a pin dropping as a type of something all but silent is from 1775.