She is a New Hampshire, yes. At least, that's my best guess from experience. I had two hatchery NH hens awhile back. The black in the tail and the lack of lots of white are what indicate NH rather than sexlink.
Ummm...what am I missing here? Yes there is a breed called New Hampshire Red. I have two. It is even listed on the breed index here on BYC, on McMurray's site, on Meyer, Ideal...
The APA does not call them by the "red" part in the name, nor do breeders. You have to consider that the breed pages on BYC are created by members, most of which having production stock, which comes from hatcheries who started the false name. New Hampshires are extremely rare, so there are very little people who correct it. kathyinmo is the only one on BYC who I know of who has true New Hampshires. . . Otherwise, if they were more, we'd fix those mistakes like we did with the misnaming that hatcheries still do of "Americauna/Americana" - And even still then, there are some BYC breed pages of Ameraucana showing Easter Eggers.
It's all about who was told what by the hatcheries and who wasn't. If Ameraucanas were as rare, we'd still believe that hatcheries carry them, that they're called "Americaunas," and that brown ones with black pencilling is accepted, since websites show it. True New Hampshires, though, are very rare, so people instead turn to the hatcheries, who call them New Hampshire Reds, and likely cross other "red" breeds into them.