Yes, there is historical basis. There are some named swords that we know about from history and also in fiction from the Middle Ages.

Charlemagne had a sword named "Joyeuse," which in French means "Joyous." There is a medieval sword displayed today in the Louvre which is known as Joyeuse and has been used for the coronation of French Kings. However, it most likely isn't the exact same one used by Charlemagne because he died in the early 9th Century, but the sword in the Louvre has a blade which is dated to around the 10th Century.

Saint Ferdinand III, King of Castille, had a sword named "Lobera," which in Spanish means "Wolf Slayer" or "Wolf Huntress."

And named swords appear frequently in medieval fiction, so it must have been a convention well-known to medieval audiences.

In the early medieval poem Beowulf, a sword given to the titular character is named "Hrunting":

"The brehon handed him a hilted weapon, a rare and ancient sword named Hrunting. The iron blade with its ill-boding patterns had been tempered in blood."

In the 12th Century fictional History of the Kings of Britain, Arthur's sword is named "Caliburn," which would of course be later known as "Excalibur." The original name was "Caledfwlch," Welsh meaning "hard cleft."

"...and across his shoulders a circular shield called Pridwen... He girded on his peerless sword, called Caliburn, which was forged in the Isle of Avalon. A spear called Ron graced his right hand: long, broad in the blade and thirsty for slaughter."