When a Party is created a label is generated for it automatically. It is possible to specify how this label is generated by configuring any number of 'Party Name Label' plugins.

At Admin > Configuration > Party > Label Plugins you can sort and modify settings for these plugins. For example, the 'attached entity field' label plugin will allow you to use a field from a data set to use for the label - thus a 'Name' field on an attached profile2 entity could be used.

The order in which the plugins are placed is the order of preference in which they will be used to label party entities. The first plugin to return a label is used for a party, so for example, for parties that do not have attached users, username will not work, but the pid example will.

Attached Entity Field
The attached entity field label plugin allows you to select a field attached to one of your datasets as a party label.
Pid example
This is a simple plugin that labels party entities with an incrementing number. eg. The 24th party in the database is 'Party 24'.
Username
This is a plugin from the party_user module that uses the username given to a main User Account. This label plugin is most effective when creating party entities automatically on user registration.