Meaning "causing infamy" is from 1550s. As a legal term, "disqualified from certain rights of citizens because of conviction for certain crimes" (late 14c.). The neutral fameless (in the sense original to infamous) is recorded from 1590s. Related: Infamously.
*bhā-; Proto-Indo-European root meaning "to speak, tell, say."
It forms all or part of: abandon; affable; anthem; antiphon; aphasia; aphonia; aphonic; apophasis; apophatic; ban (n.1) "proclamation or edict;" ban (v.); banal; bandit; banish; banlieue; banns (n.); bifarious; blame; blaspheme; blasphemy; boon (n.); cacophony; confess; contraband; defame; dysphemism; euphemism; euphony; fable; fabulous; fado; fairy; fame; famous; fandango; fatal; fate; fateful; fatuous; fay; gramophone; heterophemy; homophone; ineffable; infamous; infamy; infant; infantile; infantry; mauvais; megaphone; microphone; monophonic; nefandous; nefarious; phatic; -phone; phone (n.2) "elementary sound of a spoken language;" phoneme; phonetic; phonic; phonics; phono-; pheme; -phemia; Polyphemus; polyphony; preface; profess; profession; professional; professor; prophecy; prophet; prophetic; quadraphonic; symphony; telephone; xylophone.
It is the hypothetical source of/evidence for its existence is provided by: Greek pheme "speech, voice, utterance, a speaking, talk," phōnē "voice, sound" of a human or animal, also "tone, voice, pronunciation, speech," phanai "to speak;" Sanskrit bhanati "speaks;" Latin fari "to say," fabula "narrative, account, tale, story," fama "talk, rumor, report; reputation, public opinion; renown, reputation;" Armenian ban, bay "word, term;" Old Church Slavonic bajati "to talk, tell;" Old English boian "to boast," ben "prayer, request;" Old Irish bann "law."
1530s, "act or practice of offering the body to indiscrimninate sexual intercourse for hire," from French prostitution and directly from Late Latin prostitutionem (nominative prostitutio) "prostitution," noun of action from past-participle stem of prostituere "to expose publicly to prostitution" (see prostitute (v.)). Figuratively (of abilities, etc.), "act of devoting or offering to a base or infamous use," by 1640s.
Old English sweart "black, dark," of night, clouds, also figurative, "wicked, infamous," from Proto-Germanic *swarta- (source also of Old Frisian, Old Saxon, and Middle Dutch swart, Dutch zwart, Old Norse svartr, German schwarz, Gothic swarts "dark-colored, black"), from PIE root *swordo- "dirty, dark, black" (source of sordid). The true Germanic word, surviving in the Continental languages but displaced in English by black. Of skin color of persons from late 14c. Related: Swartest.