Gun or Gunn is an old name formed from gunnr (battle) and is cognate with the Old English word "gúð". Gunnr is one of the valkyries. The equivalent male name is Gunnar.
The earliest attestation of the name is on the Rök runestone where it occurs as part of a kenning for wolf: I say this the twelfth, where the horse of Gunnr sees fodder on the battlefield, where twenty kings lie...
Gun is the 56th most common female name in Sweden as of December 31, 2008,Given names, women (statistics from Statistics Sweden) when 34,655 living people were named Gun in Sweden.Name statistics (at Statistics Sweden)
Famous Guns Gun, a character from the horror comic series Witch Creek Road Atthaphan Phunsawat, also known as Gun Atthaphan, Thai actor Gun Adler, actress Gun Nathalie Björn, Swedish footballer Gun Andersson, actress Gun Arvidsson, actress Gun Carlson, politician Gun Fors, actress Gun Hellberg, actress Gun Hellsvik, Swedish minister for Justice Gun Holmquist, actress Gun Holmqvist, actress Gun Jönsson, actress Gun Kessle, artist, married to Jan Myrdal Gun Korawit Boonsri, Thai actor Gun Lund, dancer and choreographer Gun Robertson, actress Gun Skoogberg, ballerina Gun Chartree Sithananun, Thai guitarist
References
General sources English etymology of Norse names, referencing other names with gunnr root Swedish-language source