Can I be part of the international Jewish family but have an Arab heart?

I realize that it's a teenage cliche to have an identity crisis. So don't worry. This is not a crisis. It's just a question.
I find sometimes that I live in two worlds:  I live in a Jewish home. I speak excellent Hebrew and decent Yiddish. I go to shul. I have a deep-rooted belief in God and am a staunch supporter of Israel.  On the other hand, some of my best friends are Egyptian Muslims. I am learning Egyptian Arabic. I am passionate about Middle Eastern history and culture, which does, of course, include Israel, but also includes Jordan, Saudi Arabia and Morocco. On my bookshelf, books of Naguib Mahfouz stand next to Amos Oz next to Sami Michael next to Mahmoud Darwish. I am an extremely proud Jew, but at the same time, I am deeply interested in the Arab world, and often the parts of it that are anti-Semitic. 
I like to call this the "Leora-Noor" paradox. (It's not a paradox, really, but it sounds cool, no?)
Why do I call it that?
While this is a simplistic and untrue dichotomy, let's divide my Jewish and Arab "worlds" into two time slots: "when Leora speaks Arabic" and "when Leora speaks Hebrew."
When I speak Hebrew, I speak to Jewish Israelis 90% of the time. To them, I am Leora Eisenberg. I am just like them, I am Jewish. I am family. I can discuss politics freely and reveal my religion without fear. I can be Leora Eisenberg and not really worry about it. (As luck would have it, I was speaking to an Israeli friend of mine today, and he asked me what I consider myself. I said that I am an American with Russian parents, but first and foremost, I am Jewish.) 
When I speak Arabic, I speak to Egyptian Muslims 100% of the time. What's funny is that Arabs cannot pronounce my name. Something about putting "ee" and "oh" together has my name come out sounding more like "Leuuuuura" than "Leora" so they just call me "Noor" since it means the same thing as Leora does (light), but is more Arabic-friendly. Since my friends in Egypt don't really recognize Leora Eisenberg as a Jewish name, I've never had any issues, but I don't exactly go around advertising my religion. (In the past when I have mentioned that I am Jewish, it has rarely been a problem. The only time it was ever a major problem was the anti-semitic bashing I faced which is described in my first blog post.) I NEVER discuss politics. EVER. When I am Noor, I am an American who speaks Arabic, but I don't reveal I'm Jewish until it is absolutely necessary.
Can Leora and Noor coexist? 
Leora is my name after all, but it is also representative of my heritage. Leora is a Jewish name. I don't plan on changing it. I like Leora, and when my Arab friends can pronounce it, I go with that. But when they can't, I switch to Noor. Nothing about me changes other than my name and behavior regarding my religion and political beliefs. Is it really possible, though, to go on like this? Can I be Leora and Noor at once?