ASP.NET Repeater bind List<string>

Just use <%# Container.DataItem.ToString() %>

If you are worried about null values you may want to refactor to this (.NET 6+)

<asp:Repeater ID="repeater" runat="server">
    <ItemTemplate>
        <%# Container.DataItem?.ToString() ?? string.Empty%>
    </ItemTemplate>
</asp:Repeater>

Note if you are using less than .NET 6 you cannot use the null-conditional operator Container.DataItem?.ToString()

Set the ItemType to System.string

<asp:Repeater ItemType="System.string" runat="server">
    <ItemTemplate>
        <%# Item %>
    </ItemTemplate>
</asp:Repeater>

rptSample.DataSource = from c in lstSample select new { NAME = c };

in the repeater you put

<%# Eval("NAME") %>