CARRICK-ON-SHANNON, Ireland — A bold black-and-red sign announces Jamshid Ghafur’s business — “Kurdish Barber” — up a narrow flight of stairs just off the main street of Carrick-on-Shannon in western Ireland.

Here, patrons have their hair trimmed under the watchful eyes of the famed Irish fighter Conor McGregor, whose poster hangs high on a wall. On the opposite wall hangs a Kurdish flag, the décor a simultaneous nod to Mr. Ghafur’s homeland and the town where he lives.

“I am happy with this small business,” he said as he gestured around the shop with pride. “I feel like home here.”

Mr. Ghafur, 37, is part of a thriving group of Kurds who adopted this small town as their own after a United Nations-supervised refugee resettlement program brought them here more than a decade ago.