The Romans themselves, in their early days anyway, had very strict rules about naming each other. And they would never have used Laura as a name - they didn't choose names for their daughters the way we do, they used family names. Their word for a laurel tree (the ones that the wreaths were made of) was Laurus, and Laura makes it look more girly to our eyes, though the Romans saw Laurus as feminine.
So, your name started off as a Latin word, and became used as a name in Italian (Petrarch's beloved), Spanish, English etc. Now we can say it's used in European languages, not just the ones descended from Latin. It depends on whether people are thinking about its origin, or its usage today.