Nah. You don't have to change your name at all. There is no rule saying you have to. I won't for several years and when I go back to the states, I may. I may not, it just depends. I don't go by my birth name anyway, even though Erin/Aaron is unisex. But I may not change it. At this point I don't see a pressing need to. Even with my middle name being Whitney, I knew two different guys named Whitney so eh.
If you like it, keep it.