Since this isn't imaged very often, it doesn't have a common name that I am aware of. But to me, it looks like a swallow because of the subtly split tail of the nebula. Hey, someone has to name these things!
NGC 6991 is centered to the left of the nebulosity and includes the area where IC 5076 is located. There are two distance measurements given in Simbad, one for 700 parsecs, and the other for 1400.
IC 5076 is thought to be some 5700 light years distant (1750 parsecs) according to Wikipedia. The bright star located within that is causing it to shine is HD 199478, a variable star that varies between magnitude 5.65 to 5.84.