It's not related to
Bryce, but is a respelling of Briseida. Briseida is the Spanish form of Briseis, Greek “daughter of Briseus.” Briseus possibly meant “weighty, strong.” In the Greek legends of the Trojan War, Briseis was a young Trojan widow taken as a spoil of war by
Achilles. In romantic versions of the story, she is often presented as being in love with him. Though Briseida has never been extremely common in Latin
America, it has certainly been used more often there than Briseis has been in English-speaking countries.