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 selected name preset (see below). If you selected Leg and specified Pirate-Right, you’ll get Pirate-Right-Ankle, Pirate-Right-Hip and Pirate-Right-Leg.
The suffixes that Limber applies to your layer names - Ankle, Hip and Leg in the example above, are stored as presets. To edit presets, or add new ones, click on the Preset Editor button (the gear icon) next to the Preset Dropdown. Select a preset and you can remove it using the - button, or add a new one with the + button. You can change the display order of presets by clicking the up or down buttons. You can edit a preset in the textfields on the right. Presets are saved locally when you hit OK.
The Rename button will change the suffixes (Ankle, Hip, Leg etc) of all the layers in the selected set with those from the currently selected preset in the dropdown, as appropriate. So in our example, we could select the Pirate-Right-Hip layer, and with the Arm preset selected, click Rename. Limber would then rename Pirate-Right-Ankle, Pirate-Right-Hip and Pirate-Right-Leg to Pirate-Right-Wrist, Pirate-Right-Shoulder and Pirate-Right-Arm respectively. 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.