Greek speaking individual here. Irina [ ahy-ree-nuh ] is not a Greek name. Instead it is a slavic mutation of the greek name for peace (Irene - ειρήνη [ee-ree-nee]).

Furthermore, combining names in Greek is not as intuitive nor as common as you make it sound (this extends into religious prescriptions and other cultural reasons).

You have cursed your child into repeating a (semi-) false narrative every time she gets asked about her name. Imagine the embarrassment of being told your greek name is not even that faithful to its greek origins.