Peregrine is considered to be an elegantly aristocratic name in England, but has never made it to the U.S., where it has been seen as extravagantly eccentric. In the new naming climate, though, it's not beyond consideration — in fact it's already been chosen by at least one Berry.
The meaning of Peregrine, which was borne by several early saints, relates to the transitory nature of life on earth, having nothing to do with the peregrine falcon. In literature, it is best known from the central character of Tobias Smollett's novel Peregrine Pickle.
Historically, Peregrine was the name chosen for the first English child born in the New World — actually on the Mayflower when it was docked in Provincetown.
And there's always the Mad Men-era nickname Perry to make Peregrine more user-friendly.