"word pronounced and perhaps spelled the same as another but different in meaning," 1807, from French homonyme and directly from Latin homonymum (Quintilian), from Greek homonymon, neuter of homonymos, from homos "same" (see homo- (1)) + onyma, dialectal form of onoma "name" (from PIE root *no-men- "name"). Related: Homonymic.
"word having the same spelling as another but with a different sound and meaning," 1889, also "a thing's name in one language that is an exact translation of its name in another" (1885); from hetero- "other, different" + -onym "name" (from PIE root *no-men- "name"). Distinction from a homonym is that a homonym has not the same spelling. Related: Heteronymic; heteronymous.
word formed from the first letters of a series of words, 1943, American English coinage from acro- + -onym "name" (abstracted from homonym; ultimately from PIE root *no-men- "name"). With the exception of cabalistic esoterica and acrostic poetry, this way of forming words was exceedingly uncommon before 20c. For distinction of usage (regretfully ignored on this site), see initialism.
for historical evolution, see V. Used punningly for you by 1588 ["Love's Labour's Lost," V.i.60], not long after the pronunciation shift that made the vowel a homonym of the pronoun. As a simple shorthand (without intentional word-play), it is recorded from 1862. Common in business abbreviations since 1923 (such as U-Haul, attested from 1951).
The substitution of Middle English -o- for Old English -u- before -m-, -n-, or -r- was a French scribal habit before minims to avoid misreading the letters in the old style handwriting, which jammed them together. The practice transformed some, come, monk, tongue, worm.
Popularized in England in children's literature from early 19c. as a name for red-capped German and Swiss folklore dwarfs. Garden figurines of them were first imported to England late 1860s from Germany; garden-gnome attested from 1933. Gnomes of Zurich for "international financiers" is from 1964.