The following information was copied from the below website with grateful thanks to the team at Scots web.
https://www.scotweb.co.uk/info/gunn/

Gunn

Clan Gunn is a Scottish clan associated with northeastern Scotland, including Caithness and Sutherland as well as the Orkney Islands.The clan’s origins stretch over the sea to Norway, and the Clan Gunn themselves claim descent from the legendary Sweyn Asleifsson, the so-called ‘Ultimate Viking’, the progenitor of the clan, and through his grandson Gunni, considered to be the “namefather” of Clan Gunn.

Origins of the clan

The origin of the name Gunn is Norwegian. The word “Gunni” in the Old Norwegian language means “War” or “Battle”.

The clan’s origins stretch over the sea to Norway, and they claim descent from the legendary Sweyn Asleifsson, the so-called ‘Ultimate Viking’, the progenitor of the clan, and through his grandson Gunni, considered to be the “namefather” of Clan Gunn. They gained their land in Caithness and Sutherland through marriage to Ragnhild, from whom they can claim Celtic descent, and later expanded those lands through conquest. However, the Gunns were never a large clan, and soon found themselves in conflict with several more powerful neighbours, such as the MacKays and the Keiths. The clan concluded a peace treaty with the latter of these in the year 1978, officially bringing to an end a feud dating back more than five hundred years.

Those who did stay in the traditional boundaries were among the line descended from a younger son of George Gunn, Robert Gunn, who was the progenitor of the Robson Gunns of Braemore, though it is not clear how these names came to pass. One theory points to the Norse and Celtic origins of the Clan, using suffixes to denote the order of male children; with “in being second son”. It is a difficult line to track as Gunn and other names of this line are used interchangeably in old text. Other branches remained as well moving to the Strath of Kildonan and other locations in Caithness.