Looking for Bourke/Burke and Ware connection

I have two ancestors from Limerick City. Hugh Ware Bourke and James Ware Bourke. Both were hairdressers in the early 1800s in Limerick City. It is very possible they have connections to Galway and/or Tipperary.

I don't know their relationship to each other, but presuming it's a family name. Hugh Bourke's mother was Matilda Cox.

Just throwing it out there!!!!!!!