There is a beautiful, if somewhat stained, bas-relief of the Archangel Gabriel on one of the well-heads in Campo Sant' Angelo. And the small church of Sant'Angelo degli Zoppi, which sits in the corner of the square, is also known as the Oratorio dell'Annunciata. So it would seem safe to conclude that Gabriel is the angel after which the campo is named. However, this is not the case.
A small plaque in the campo marks the spot where the church of San Michele Arcangelo once stood before it was destroyed, in 1837.
The church can be plainly seen in this painting by Canaletto:
The church had first been dedicated to San Mauro, but a century later it was re-dedicated to San Michele Arcangelo. However, the Venetians would always refer to it, simply, as Sant'Angelo.