Well, it’s a bit literary or fannish for your parents to name you Arwen, and Tolkien, as a good Catholic, probably would have voted for a normal given name, with Arwen as a nickname (or “epessë“) if needed. And it’s likely that you’ll have a separate baptismal name somewhere if you got more than just a first name out of the deal, like most parents would do.
But if you are looking to find out who the patron saint or nameday saint of people named Arwen would be, just look at the name. Arwen means “royal maiden” or “royal lady” in the invented language of Quenya. So all you need are saints’ names that mean “princess” or “queen” or “royal,” and we’ve got them. (But don’t try to pick Arwen as a confirmation name, okay?)
Obviously, the Virgin Mary herself has pride of place here. She is a princess and queen mother of the House of David and of Heaven.
There’s also St. Regina, a convert in Gaul martyred for refusing an arranged marriage and fleeing to become a shepherdess. Her feastday is Sept. 7.
St. Rioghnach daughter of Feradhach was listed in the Martyrology of Donegal. (Dec. 18) Her name also means “royal” and therefore she is called “Regina” in Latin. She was the sister of St. Finian of Clonard.
Then there’s St. Basila, a Roman martyr (Sept. 22), several Ss. Basilia, including one martyred in Alexandria with Origen’s dad (April 22), and several Ss. Basilissa and Vasilissa. The Greek name for king is “basileos.”
Anyway, there are probably others I’m not thinking of, and of course there are lots of princesses and queens who became saints.
So yep, there are name saints for those of you named Arwen! Feel free to celebrate your name day on their days!
UPDATE: If anybody named their kid “Undomiel” or “Evenstar,” then you should know that the evening star (ie, the planet Venus seen in the evening) is “hesperos.” So your name saint would be St. Hesperus of Pamphylia (May 2), the father of a family of slaves who all refused to sacrifice to the gods and were martyred for it.