Henry Barber in his history of British family names, says:-

aunt minerva collection
The Foster Family by W.T. Foster cont.
THE BRYANT FAMILY
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"The name Bryant is from Breaunt, a locality in Normandy. The French name was Briand, which was changed into the English Briant." Parke Goodwin, the historian of William Cullen Bryant the poet, statesman, scholar, and editor, says that the name Bryant means broad hand, a chieftan, great strength. William Cullen Bryant was cousin to Jonathan M. Bryant, my wife's faterh. Barber further says that a coat of arms was granted Thomas Bryant by the English government in 1634. I give that crest in the Bryant coat of arms. The descendants of Thomas Bryant came to America.
Stephen Bryant came from England 1632 and lived at Plymouth, Mass. where he was a prominent citizen, filling many public positions. He was the son of the above named Thomas Bryant. This Stephen Bryant married Abigail Shaw who came from England in 1632 and settled at Plymouth, Mass. From this couple the Bryants of America are descended. Stephen Bryant, son of the above lived at Plymouth, Mass. in 1640 and married Sarah Snell, a descendant of John Alden, a Pilgrim Father, who came over in the Mayflower and was long the Magistrate-the court's judge-at Plymouth. John Alden signed the compact of the Pilgrim FAthers before he left the Mayflower at Plymouth. His wife was Pricilla Mullins, 1621-and is celebrated in Longellow's Miles Standish. One of John Alden's descendants was author and owner of Alden's Cyclopedia-one of the best-forty volumes, a set of which I have owned and relied upson since 1887. By above it will be seen that the American Bryant's are descendants of the Pilgrim Fathers. For that reason I include the Plymouth Rock in the coat of arms of the American Bryants.