Well that's the thing about common names, you can never really know. Should we all switch to latin? haha.
all kidding aside, usually I think people talk about hophornbeam Ostrya virginiana. It's great bow wood and, as you said, they can come in nice long straight staves. I have seem a few hornbeam Caprinus caroliniana bows around here but that tree is often gnarly and has twisted grain.
If you have a good supply of Ostrya, you have a lot of bow wood on your hands.
Cheers
Matt