Does this optical phenomenon have a name?
It appears from your picture that there is some mist above the lake surface. The phenomenon will be due to the same mechanism that causes conventional rainbows. The angles between the sun, the mist/cloud, and the observer will be identical but you will only see this with the sun low in the sky since the mist is near the water. That will also make the rainbow appear to be floating on the water surface (great photo, btw). I think the dark background of the trees helps make the colours more intense. The low sun means that the spectrum can be seen on either side and behind the observer. So you are correct that it will form a triangle around you. If I'm visualizing things properly, in your photo the sun would be to your right - on the violet side of the rainbow.

I am not aware of any distinct name for this, possibly because it is not really different from a rainbow from a scientific perspective or because too few scientists are awake at 4 AM.