"Durkin
Origin: Irish
Spelling variations include: Durkin, Durkan, Dorcan, McDurkin, McDorcan, McDurkan, Gurkin, McGurkin, O'Durkin, O'Durcan and many more.
First found in north Connacht where they were anciently seated as Chiefs of their race."
"The names Durkin, Durcan and Dorcan in Ireland are all derived from the
native Gaelic O'Duarcain and MacDuarcain Septs that were located in
Connaught Province in the West of the country and especially in County
Sligo. Gurkin is another variant sometimes used as an anglicized form
of these Sept names."
I found this info on some family history sites. Also the dictionary of Irish surnames
says that Durkin and its many variants means "a gloomy person".
Still can't find a meaning for Muirsheen though.