Ah, the name conundrum... Personally, when I first began socially transitioning (I was 13) I had a HUGE list of names that I would ask each of my friends and family to pick three from the list, and I was going to go with whichever had to most votes. My family didn't want to vote, though, because they didn't support me initially, but my friends did. And then I wound up not going with any of the names on that list.
I chose Maksim (just Max, really) because 1) it ties into my Russian heritage, and 2) the "ma" part is similar to my birth name, so it's easier to remember. My family eventually came around when they realized it wasn't going to just go away. I've been Maksim, or just Max, for 7 years (have yet to change it legally, though).
I did go through phases where I tested out different names to see if they fit, but none of them really did. It did help that I had my family and friends to call me by those names while I figured it out, but again, it just felt like I was being called by a stranger's name.
Take a while to see if Julian is a true fit, have the people around you call you by that name and if it doesn't feel like they're talking to YOU, find another. It just takes testing.