It looks like the signature says "Eugene W. Roddenberry" next to or underneath what I assume is the actual artist's scrawl.
These were a series of twelve "
Enterprise Evolution" posters offered by Lincoln Enterprises. I don't think they're actual production art, but were created after the fact as merchandise based on the original black-and-white design sketches. So I doubt the signature next to Roddenberry's is Bachelin's.
Here's the text describing them from the one remaining Lincoln Enterprises catalog I have (probably from 1983, since it only has merchandise up to TWOK):
The Enterprise was not created overnight. In fact, there were eleven other designs -- all sporting the name "Enterprise". We've dug into the archives and come up with -- you've guessed it -- twelve Enterprises -- all very different -- all very exciting. We call our fleet "The Evolution." This package of twelve 11x17 full color posters can now be yours. A truly exciting offering.
The set of twelve posters was offered for $4.95.
There are only eleven shown here. The reproductions in the catalog are tiny and crude, but it looks like the twelfth one was a variant or simply another angle of the one with four nacelles, a sphere, and a disk (the seventh one from the top in
NCC-1701's post). So the catalog text claiming twelve very different
Enterprises is inaccurate (and I'm sure some of these weren't called
Enterprise, since the ship was called the
Yorktown for much of the development process).
EDIT: Oh, wait -- read the text more closely on that CafePress page:
The 11 different treatments of the Enterprise were signed by Eugene Roddenberry, Jr., and will be reproduced in a limited run for your Star Trek collection.
So the signature is "Rod" Roddenberry's, added very much after the fact. Apparently Roddenberry.com, the successor to Lincoln Enterprises, is putting these back into print -- and stating an outright falsehood when it says they're "made available to you for the first time." And they're charging a grand total of $549.89 for 11/12 of a set you could get for less than five bucks in the '80s.