Register

The word register can have several meanings. Very often it means: something that is written down so that there is a record (written proof) of something. It may, for example be a list of names. 
It can also be used as a verb: to register, i.e. to write something down in an official register (e.g. a special book), e.g. to register a birth, marriage or death. 
Registration is the act of registering or being registered.