The most common advice for picking a Hebrew name:
- A Hebrew equivalent of your English name (which probably doesn't exist)
- A Hebrew name that starts with the same letter as your English name
- A Hebrew name with the same meaning as your English name
So here's my suggestion: look up Jewish baby names (there are oodles of websites of baby names, as well as Jewish-specific books in the stores) and make a list of all the names that speak to you, either through their sound or meaning. You don't have to take a Biblical name, though that is very common among converts. Let that list marinate for a while. For that reason, I recommend making the list early in your process and adding new names as you go. Others, particularly those working with you during your conversion, will recommend names. I suggest adding them to your list, even if you don't like them at first. After all, they should know you well and maybe have some insight into a name that will fit you.
Review the list periodically. Roll the names around in your mouth. Feel free to try one out as an everyday name for a few days.
Run the list of names past someone else pretty early in the list-making process. I was so attached to a name for almost 2 years. But when I told my rabbi at the time, he advised me that it's a "H" v. "CH" away from being the word "disease." And that in modern Hebrew, it's the word for cancer.
When you know you're getting close to the end of your conversion process, take that list back out and see which names still resonate with you.
It's a very personal process, and we all approach it in a slightly different way. You and only you can choose the right name. Don't let someone (even a rabbi) push you into taking a name you don't want. A push is probably well-meaning because they just know the right name for you. It's been known to happen in all movements (and anecdotes suggest this is more common in the liberal movements), and it usually results in some pretty negative feelings after the fact.
Don't be worried if you're surprised by the name you eventually choose! I was!
Happy name hunting!