The oe in amoeba is a Greek diphthong that came through Latin and stayed put. The Greek is amoibē, "change, alteration, exchange," related to a verb meaning "to change" — the creature is named for the fact that it will not hold a shape. Like aesthetic and oesophagus, the word keeps a two-letter vowel spelling that English pronunciation flattened long ago, and American spelling often simplifies it to ameba.
It is also a reminder that Greek-looking words are frequently modern inventions rather than ancient inheritances. Nobody in Athens called anything an amoeba. The word is Modern Latin, coined as a genus name around 1830 by the German naturalist Christian Ehrenberg and in English from 1841, assembled from Greek parts by a nineteenth-century scientist who needed a name. The older popular term for the animal was proteus, after the shape-shifting sea god — the same idea, borrowed from mythology instead of grammar.
amoeba (n.) type of microscopic protozoa, 1855, from Modern Latin Amoeba , genus name (1841 in English, said to have been used 1830 by German naturalist Christian Ehrenberg), from Greek amoibē "change, alteration; exchange," which is related to ameibein "to change, exchange" (from an extended form of PIE root *mei- (1) "to change, go, move"). So called for its constantly changing shape. An earlier popular name for it was proteus (1660s). Related: Amoebic ; amoebiform ; amoeboid . also from 1855
amoeba came in through Greek, and its spelling follows that family's conventions.
How that family writes these sounds
| /iː/ or /ɛ/ in an old learned word | ae or oe — American spelling simplifies both to eaesthetic, amoeba, oesophagus |
What gives it away on the page
| ae, oe | Greek diphthongs through Latin. American spelling often simplifies them to e.aesthetic, amoeba, oesophagus |