If you already have a "Jewish name" and you like it, then you don't have to change your name! Rachel becomes Rachel, and Rebecca becomes Rivka.
However, some rabbis may insist that you use a different name in order to separate yourself from your prior life and because of the precedent of Avram and Sarai (changed to Abraham and Sarah). Some rabbis (and other people) object to this "requirement" because there is no evidence that Ruth, the most famous of converts, changed her name. I personally think that you should have the freedom to either make a break with your "former life" or to embrace this new stage as the natural continuation of your identity. A name can strike to the root of your identity, and that is nothing to play with for ideological reasons that aren't required by halacha. (Those "ideological reasons" being that your "non-Jewish" past is inherently a bad thing that must be rejected and hidden.)
Of course, you can always choose a totally different Hebrew name if you want to. In fact, at least two of my friends have had "Jewish-appropriate" English names and chose different Hebrew names. It caused some confusion for me at first, but maybe I'm just confusion-prone. Whatever temporary confusion there may be, you need to choose the name that resonates with you. Only you have to live with this name.
Likewise, it is your choice whether you use your Hebrew name on a daily basis or whether you only use it when halacha requires.
And remember that you can have more than one name in your Hebrew name! Let's look at some examples.
So... what if your English name is Rachel Talulah? You could choose some of the following names:
Rachel bat Avraham
Rachel Tirtzah bat Avraham (keeping the sound of Talulah)
Leah bat Avraham
Yael Yocheved bat Avraham
Irit Chaya Shira bat Avraham
Get it? The world is your oyster! (Except not, because oysters aren't kosher.)