Working out the correct man is quite a tricky thing to do especially with common names.
Many of the papers - especially later ones - have very little information.
As you say, Next of Kin - parents, marriage or children etc is one way to work it out but there are other bits of info which can prove useful too..eg
Birth year , birth place, address at enlistment, sometimes there is an address on discharge, occupation is sometimes listed and sometimes has info of where they worked (not often). And there may be distinguishing marks noted which just once in a while can show you have the right chap
Pension records if there are any have more info on them than basic enlistment (attestation sheets) eg about where they intend to work and correspondence about any injuries or medical treatment etc.
First thing is to see if there are any papers which may be his... and often the only way is to open every single one of the right name and look through them (not ideal if he is called John Smith)

As Carole says - let us have some detail and we can advise further.
Milly