No, there is no angel named Nathanael mentioned in the Bible.
The name Nathanael (or Nathaniel) appears in the New Testament as the name of one of the original disciples of Jesus (John 1:45-49, 21:2). He is sometimes identified with Bartholomew, but this is a matter of scholarly debate.
While the Bible mentions several archangels like Michael and Gabriel, and some other angelic beings are named in apocryphal or pseudepigraphal texts (books outside the accepted biblical canon), Nathanael is not among them.