You guys nailed it!
Ralf is technically correct on the C6 - Eb6 nomenclature. When you strum open in GCEA, for example, you get a C6 chord. As a matter of convention, however, the "6" is generally dropped. It's assumed that if the tuning is in 4ths (4 note intervals), as are all standard ukulele tunings, that an open strum is a 6th, and so the tunings are just referred to as key of C, etc. - in this case Eb.
An even easier way to look at it is that the third string is the name of the tuning. G
C EA is key of C while Bb
Eb GC is key of Eflat.
Apparently the earliest Hawaiian instruction manuals used Eb, D & C tunings. It was after the turn of the century, on the mainland, where Breen promoted D tuning - what then was known as "standard". Eb was also the suggested tuning for the first Sopraninos.
As OldePhart noted, it is usually easier to play, and often sounds better, to have your tuning match the key of the song, and Eb compositions are not uncommon. Capos are a nice option for switching between the high tunings (especially with a long-neck soprano), and finally, either of our Light Gauge string sets will handle this tuning nicely on a standard soprano scale:
http://www.southcoastukes.com/stringuide_files/ltuke.htm
You can "pull them up" from D and relax them back down again.