I have found a swapper but their name does not show up on my swaps page...

If they do not have an email address set they will not show up on your swap page

If they have no email set, they cannot be contacted, so they are not shown. Saves time!

Do they have the same album type?

If you are collecting: Merlin Premier League 2008

and they are collecting Merlin Premier League 2007

the name will not show up on your swaps page.

You will need to find a mutal album (one that you are both collecting) in order to see any swap opportunities.