You can't unfortunately. I would recommend you contact API support and have yourself added to SPR 750541: "Need an ISketchRelation API which gets the sketch relation name".
Now, if you're only concerned about stating the relation type as a string, ignoring the instance number, then you could use a Select Case statement and for each relation type, return a string.
Thanks once again Keith.
I can get the type of relation but not the specific name.
How do I get added to the SPR?