Filbert is an alternative name for a hazelnut. The present spelling came into usage in the late fourteenth century. It derives from the Anglo-French word philber, which comes from the Norman phrase noix de filbert, meaning literally “nut of filbert.”
So who was this Filbert guy? The name refers to Saint Philibert of Jumièges, a Frankish abbot and monastic founder who lived from circa 608 to 684. Born in Gascony, Philibert was the son of a courtier and became a monk at Rebais Abbey. He received a gift of land from Clovis II in 654 and founded Jumièges Abbey near Fontenelle, France. He later founded other religious houses including the monasteries of Noirmoutier and Cunaut and a nunnery at Pavilly. His remains were buried at Noirmoutier but Viking attacks drove the monks inland to the abbey at Tournus, where they installed his relics at the church of St Philibert at Tournus.
Saint Philibert had nothing in particular to do with hazelnuts during his lifetime. (I suspect he ate some but that remains unsubstantiated speculation.) The connection comes from his feast day, August 20th, which is about the time that hazelnuts ripen.