'anagram-related' originates from modern English compounding of 'anagram' + 'related', where 'anagram' ultimately comes from Greek 'anagramma' (ἀνάγραμμα) meaning 'a writing up again' or 'rearranged letters', and 'related' comes from Old English/Latin roots meaning 'connected'.

'anagram' entered English via Medieval Latin/Old French from Greek 'anagramma' (from ana- 'again' + gramma 'letter'); 'related' derives from Latin 'relatus', past participle of 'referre' ('re-' + 'ferre' meaning 'to carry'). The compound 'anagram-related' is a modern English adjective formed by joining the noun and adjective.

Individually, 'anagram' originally referred specifically to a rearrangement of letters; over time it retained that meaning, and the compound 'anagram-related' simply combines that sense with 'related' to mean 'connected with anagrams' in contemporary usage.