There are a few contexts involved .... signature being derived from the Latin signare (I write) A Standard signature is usually initials and name, written by the same person, and usually stylised, but it can be a mark or symbol, by which the signing person can be identified..... even a "X". A signature can also be a trademark eg McDonald's golden "M" or it can be a sound eg a signature tune for a performer. In all cases it must belong to and identify the user only.
A mark or sign made by an individual on an instrument or document to signify knowledge, approval, acceptance, or obligation. That's probably the reason we should watch what we sign, there is a legal binding once any document has your signature.
1st rule have a pen 2nd rule have some paper 3rd rule get someone to sign it