The name, Taryn, is usually known to mean 'Thunder'. English and Welsh in origin meaning from a high rocky cliff. While a lot of people think that Taryn is an exclusively new name, it was often used in Ireland as early as the 1700s as a combination of the Names Tara and Erin..Tara, meaning hills, and Erin, meaning Ireland.s a kid, I was told that I was named after the actress Taryn Powers. She was the daughter of Tyrone Powers, a fairly famous actor back in the 1940's-1950's I think. Supposedly, Tyrone intended to name his child Tyrone Jr., but when a girl was born, he feminized his name and created Taryn.