These two Welsh beauties both mean "snow white," from the elements eir, "snow," and wen, "white." Neither was used in the U.S. in 2011 (or ever, I'm certain). White Pages tells me there are no living people in the U.S. named Eirawen and only 4 named Gwyneira. Eirawen is pronounced EYE-rah-wen, Gwyneira is pronounced gwin-EYE-rah. The South Wales pronunciation for Gwyneira is gwin-AY-rah, and a lesser used spelling is Gweneira. The girl's name Eirwen also means "snow white" in Welsh. Eirwen is AYR-wen in South Wales, and IYR-wen in North Wales.
The Old Norse female name Eir (AYR, rolled-tongue on the R) belonged to the goddess of healing in the Norse pantheon, and the name meant "mercy, healing." It is still used in Iceland and Norway. The variant Eira, separate from the Welsh name, is also used in Finland, Norway and Sweden. In Norway, she last ranked at #99 in 2013, as well as Sweden and Finland.
The goddess Eir was written about in Svipdagsmal, Prose Edda and Poetic Edda (where she is a member of the Norse pantheon in both writings), as well as other skaldic poetry and runic writings. I wrote about Edda as a name as well. Some say Eir was in fact a poetic form of the goddess Frigg, but in some cases she was an attendant goddess. She was a valkyrie, too. Instead of choosing the fallen soldiers to take to Valhalla, she chose those who would be healed and recover.