I always thought I'd pick Ezra. I have always been inspired and gotten chills when I think about the impact that he had on Judaism, starting to read the Torah publicly in the midst of a Jerusalem being rebuilt. But my son really liked that name so I went back and looked for another one and opted for Yohanan. For the last 450 years a somewhat similar name (Johan) has been in my family for men (alternating with Jacob from generation to generation) and I felt it was a good way to link my family history with our Jewish future.
I have to laugh when I think about how I chose my Hebrew name. I read a book (I do not now remember which) that said that "all female converts" take the name Ruth. So when my rabbi asked me what name I wanted, I said, "Ruth." He said, "Great choice!" and I thought "Whew, I passed the test!" After my conversion, I found out that I had had a choice! I thought about changing the name, and thought about at all the names I might pick. Eventually, though, I realized that Ruth was the name I would have chosen all along. The Biblical Ruth is my role model: a woman who transforms her own life and the lives of those around her with kindness and good will.
I had no idea how to give myself a Hebrew name. I think I saw a limited list in an Anita Diamant book, and looked through them. I suddenly had the idea to name myself after my mother. Mom died 8 years before, and her Christian religion was very important to her. It may sound like crazy logic, but I named myself after her - Chava for Eve - in order to honor her even though I knew she would have disapproved.
This is a topic I love, since I love names and their origins and sounds. My Hebrew name is Eliezer Shalev. While quite often a Hebrew name is just one name, I chose a two-name combination, for two reasons. (1) Eliezer is a Biblical name, which means G-d's (El) helper (ezer); I've also seen it translated as G-d is my helper. I like this name for both its meaning and how it sounds. (2) Shalev is a modern Israeli name, somehow morphed out of shalom, all aspects of which I relate to. So the two-name combination bridges the ancient and the modern, the span of Jewish history as it were, and the two names sound good together to my ear. It's something I enjoyed discussing with my converting advisor, Rabbi Chester. It took me months to work it out.