There are over 370 varieties of zucchini, At least 350 of them will look like like your photo at its stage of development, It can be narrowed down later by fruit shape, fruit color etc. If it is a dark green cylindrical type it becomes next to impossible because there are so many of them. If you know which company produces the plants for your nursery, you can narrow your choices that way.

Thanks!
I will ask the nursery next time I'm in town.
Here's a fruit pic, althought difficult to see.

Bonnie plants sells Black Beauty. Anyone in the east buying from a local nursery can be pretty sure they are getting Black Beauty an open pollinated variety. Bonnie does supply plants to Richmond,El Cerrito, Pinole, Hercules so Black beauty would be a pretty good guess.

Mine is from Bonnie and had the Black Beauty label, but even then, not all the fruit from the plant looks exactly the same. If you like the variety, save the seeds.

Here is a link that might be useful: zuccini pictures

Thanks for the additional help!
The leaves sure don't look like the google images of Black Beauty.

Josh