Crow - was an American band with lead singer David Wagner
Eagle - Josef Franz Wagner, an Austrian composer, best known for "Under the Double Eagle" which refers to the double eagle in the coat of arms of Austria-Hungary. I've included the video because it is quite a well-known tune.
Seems the operas were named Ring after an actual finger ring though and woodbird is not the accepted name of a British bird. Having looked through the works of Wagner to no avail I actually think bibble's suggestion of Crow is brilliant. It's a band most people of heard of and there was no specific reason for us to assume we are talking Richard Wagner.