The PlayList control is built off the ASP.NET GridView, and fully supports templating. Please edit the template however you like.
For example, here is the default template that is generated when you drag the control onto your webform:
Code:<asp:TemplateField ShowHeader="False">
<itemtemplate>
<asp:LinkButton ID="TrackSelectButton" runat="server" CausesValidation="False" CommandName="Select" Text='<%# Eval("URL") /*Eval("TrackNumber")+". "+Eval("Name")*/ %>'></asp:LinkButton>
</itemtemplate>
</asp:TemplateField>
You can make this content be whatever you like. Noticed that I've commented some code in there - if you want the Name to show and not the URL, it should be something similar to this:
Code:<asp:TemplateField ShowHeader="False">
<itemtemplate>
<asp:LinkButton ID="TrackSelectButton" runat="server" CausesValidation="False" CommandName="Select" Text='<%# Eval("Name") %>'></asp:LinkButton>
</itemtemplate>
</asp:TemplateField>
The databinding names here (within the Eval statements) link to the default playlist data source. If you're loading playlist data from a database, the Eval("Name") should be changed to Eval("YOUR_DATABASE_NAME_COLUMN").
Let me know how you do.