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."
1560s, "distinguished by greatness, renowned," from Latin illustris "lighted, bright, brilliant;" figuratively "distinguished, famous," probably a back-formation from illustrare "make light, light up, illuminate," figuratively "embellish, distinguish, make famous" (see illustration). Replaced illustre in same sense (mid-15c.), from French illustre.
"celebrated, famous," late 14c., past-participle adjective from renounen "make (a name) famous, honored, or celebrated," c. 1400, from renown (n.). The verb is obsolete except for this derivative.