This is actually a very pretty name despite sounding made up and everything. In Finnish, this word means 'story', as in a fictional story. It wouln't be used as a name by any sane person, and I don't think it would even be legal here, but the pronunciation of the word is ''TUH-ri-nah'', and that would sound nice enough for this name, as well as ''TA-ri-nah'' would. The name could even be turned into Tarinna and pronounced with a short and stressed ''e'' sound, and it would be nice.
Tarina is a perfectly legitimate name in Finland, though not very common. It has been used through all of the 20th century and this decade hasn't so far shown any notable drop in its popularity.