From Longman Dictionary of Contemporary Englishsomething has somebody’s name on itsomething has somebody’s name on itsomething seems to be appropriate for or deserved by a particular personThe match has England’s name on it (=they will win it). →name
Examples from the Corpus
something has somebody’s name on it• They say if it has your name on it ... But who can write on a virus?• If a washerhas a brand name on it, make sure that the smoothside comes into contact with the seating.