'Signature' is Latin for 'a marking' — the unique mark identifying a person, from 'signum' (sign).
A person's name written in a distinctive way as a form of identification or authorization; a distinctive pattern or characteristic by which something can be identified.
From Medieval Latin 'signātūra' (a signing, a marking, a sign used in documents), from Latin 'signātus,' past participle of 'signāre' (to mark, to put a sign on, to sign, to seal), from 'signum' (a mark, a sign, a standard, a signal, a seal). The PIE root behind 'signum' is debated — possibly *sekʷ- (to follow, to point out) or *seǵ- (to bind, to fix). A signature is literally 'a marking' — the unique graphic mark by which a person identifies themselves and
In music, a 'key signature' (the sharps or flats at the beginning of a staff) and a 'time signature' (the fraction indicating meter) are both 'signatures' in the etymological sense: identifying marks placed at the start that define the character of what follows. A piece in E-flat major with a 3/4 time signature has its identity 'signed' before the first note is played.