From "A New History of Ireland," edited by Moody, Martin & Byrne, vol 3, ISBN 0-19-821739-0, 1976, p 71:
Ulick Burke, the recently created Earl of Clanricard, died in 1544, and, although his son and heir, Richard, succeeded him and was to have his loyalty to the crown commemorated in his appellation Sassanach (English), south Connacht was upset by the ensuing squabbles of rival Burkes.

From Irish Roots, 1994 #1, page 27, 'Surnames of County Galway':
The name Burke is one of the most numerous among Galway surnames. The Norman progenitor of the family was William FitzAdelm de Burgo who was sent to Ireland with Hugh deLacy and in 1179 received a grant from King Henry II of England of large tracts of Connacht. About 50 years later his son Richard built a castle at Galway as part of his campaign to take possession of the lands thus bestowed on his father. The surname was to spread rapidly. It became de Burgh, Burke and Bourke. But the families subdivided and became Hibernicised. They even adopted among their subsepts names such as macDavie, MacHugo, MacRedmond, MacGibbon, and MacSeoinin. The major division was between the Burkes of MacWilliam Uachter in Galway and of MacWilliam Iochtar in Mayo. Though the Burkes, or de Burgos, founded Galway city their followers, later known as the Tribes, soon tried to cast off their overlordship. Indeed the charter of 1484 issued to Galway by Richard III was to break the suzerainty of the Burkes who were not allowed to enter the city without the license of the Mayor. The major branch of the family in County Galway were the Clanricarde Burkes who were chieftains of their name and descendants of Rochard Og Burke who died in 1387. The title Earl of Clanricarde was given to the head of the family by Henry VIII in 1543. Portumna became the principal seat of the Clanricardes. Junior branches had seats at various places in Galway. They occupied many of the late medieval tower houses but later built residences such as St Clerans, near Craughwell or the Castle at Glinsk. They were to play a very important role in the 17th century wars from which the Clanricardes emerged defeated but still with very substantial estates.

During his life this Ulick had been married to different wives. He had first married Grany O'Carroll. By this wife the earl had his eldest son, Richard Bourke. He afterwards discarded Grany, and married Honora Bourke, from whom he separated, and during the life of Grany O'Carroll, he married Maria Lynch, by whom he had a son, John Bourke, who disputed the succession with Richard, his elder brother. John Bourke alleged that the earl had married Grany while O'Melaghlin, her first husband, was living--and that Richard Bourke was illegitimate. An appeal was lodged with the deputy and his Council, who appointed the earl of Ormond, and other Commissioners, to examine the case. The Commission decided in favour of Grany O'Carroll, whose son, Richard, became earl.173