Swedish. From the name of a flower, also known as the twinflower. It was named by the Swedish botanist Carolus Linnaeus, who named it after himself, it being his favourite flower (Behindthename.com)
Babynamewizard tells me it is #2 in Norway & #8 in Sweden.
New Zealand Baby Names 
shay120 said,
October 28, 2009 @ 8:32 pm
I really like the name Linnea, I know quite a few as I know a lot of Swedes.
babynamelover said,
October 29, 2009 @ 12:17 am
Do you think it suits people of all ages?
marilyn said,
October 29, 2009 @ 4:30 pm
I think it’s lovely. My sister in law used it for her baby, but they spell it “Linaya” 😦 Linnea is so much prettier, IMO.
babynamelover said,
October 31, 2009 @ 1:59 am
Linaya looks like the trendy Maya! Linnea is prettier I think 🙂