When you click New, you'll get a popup asking you to name the limb. This is so you can differentiate between limbs within a character (such as left and right) as well as between different characters. The layer names can always be altered later if you change your mind.
Limber will make a new set of layers and give each one a name based on a combination of the name you entered in the dialog box, and the preset you had selected in the name preset dropdown. If you selected the preset Leg and specified Right, you’ll get Right-Ankle, Right-Hip and Right-Leg.
The Rename button will change the suffixes (Ankle, Hip, Leg etc) of all the layers in the selected limb. To do this, it uses the names from the currently selected preset in the dropdown. So in our example, we could select the Right-Ankle layer, and with the Arm preset selected, click Rename. Limber then renames the layers to Right-Wrist, Right-Shoulder and Right-Arm. This is really handy if you duplicate a leg, intending to make it into an arm, for example.
If you Alt-click the rename button, Limber will change the prefix, so you can change Right to Left, for example.
When manually renaming limbs, it's best practice to leave the dash between the prefix and the suffix.