The dragon that gnaws at the roots of Yggdrasil is Níðhöggr, also spelled Níðhǫggr or Nidhogg.
Níðhöggr dwells beneath the world tree and attacks one of its roots, the root associated with Niflheim. In the Prose Edda, he is described as a serpent-like being, while modern retellings usually call him a dragon. His name is commonly interpreted as referring to malicious striking or a hateful attacker.
The creature appears in both the Poetic Edda and Prose Edda. In Grímnismál, Níðhöggr is one of several beings that trouble Yggdrasil. The squirrel Ratatoskr runs up and down the tree carrying hostile messages between Níðhöggr below and an eagle at the top, creating a memorable image of conflict within the cosmic tree.
Níðhöggr is not Fafnir, the dragon defeated by Sigurd, nor Jörmungandr, the Midgard Serpent associated with Thor. Regin is also different: he is a dwarf or smith in the Völsung tradition, not Yggdrasil’s root-gnawing monster.