This is so pretty! I love this name so much! I love the spelling, pronunciation, and admittedly the meaning. The meaning could lead to a person thinking that a Brynja is storng willed and not someone to mess with but the pronunciation could ease their minds because the name sounds peaceful & graceful.
We have both a Sonja and a Brynja. Most Scandinavians know how to pronounce both but it's not such a "nightmare" in school. You just tell people how to pronounce it and as you get older you can be glad for something unique and pretty.
This is actually not just a word in Old Norse, it is the word in modern Swedish for chain(ring)mail armor - ringbrynja.Other than that, it's a really nice name.
This name actually isn't that bad in terms of pronunciation and such (in the English-speaking world). Most people, even little kids, know that Sonja is SOHN-ya, so anyone named Brynja shouldn't have too much difficulty. And I like this name, actually! It sounds quite pretty.