No. There's not much in the way of named weapons/armoury in Greek mythology. The shield gets its fullest description at Iliad 7.219-23:

And Aias approached him carrying a shield like a fortress
of bronze and seven ox-hides, which Tychios made and worked for him:
he was by far the best of leather-workers, who lived in Hyle,
and he made for him a glittering shield of seven ox-hides
from strong-reared bulls, and he hammered an eighth layer on it of bronze.

The seven ox-hides" thing comes up again and again where Aias features in battle-scenes. At Iliad 7.244-8, for example:

He spoke, and brandishing his long-shadowed spear he threw it
and hit Aias' terrible shield of seven ox-hides
through the outermost bronze, which was the eighth layer on it,
and the bronze cut its way unwearyingly through six folds
and stopped at the seventh ox-hide...

The phrase "Aias' terrible shield of seven ox-hides" (Αἴαντος δεινὸν σάκος ἑπταβόειον) is repeated again at various points throughout the Iliad. Definitely not a name, though.