Not 100% sure on this since I'm not familiar with Eclipse update site building, but this page:
http://wiki.eclipse.org/Equinox_p2_Metadata_Generator
Seems to indicate you can generate the metadata for the update site using org.eclipse.equinox.p2.metadata.generator.EclipseGenerator which includes the site name as a parameter:
Arguments describing the output
[...]
-metadataRepositoryName
a user friendly name for the metadata repository
Perhaps that's what you need, to generate the metadata for the site? See http://wiki.eclipse.org/WTP/What_we_have_learned_(to_love)_about_P2 as well:
...Since you have both a content.jar and a site.xml at that location, you
actually have two repositories. You have a classic update site, and a p2
repository (these files don't know/care about each other). Classic update
sites don't contain a site name (site.xml has no name element), so these
sites are "nameless". p2 repositories contain a name element so they have
a human-readable name.