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This game has no name. It was played for centuries, then forgotten for roughly five thousand years, and the name we use now is borrowed from the city where archaeologists dug it up: Ur, the city where Abraham was born.
Nobody alive knows how it was actually played. The board survived; the rules didn't. What exists instead are reconstructions, and the one here comes from Dmitry Skyruk, a writer and board-game populariser who set out to produce a ruleset that plays as a genuine contest rather than a museum exhibit.
The result is far less forgiving than a five-thousand-year-old game has any right to be. Try it and see how you do.