Actually, looking at what you're trying to do a bit more closely, it looks like what you have is probably OK. From here, you should be able to simply bind the SelectedValue property of the DropDownList using two-way databinding, like this:
Code:
<EditItemTemplate>
<asp:DropDownList ID="DropDownList1"
runat="server" AutoPostBack="False" DataSourceID="SqlDataSource3"
DataTextField="Name" DataValueField="Name" SelectedValue='<%# Bind("Category") %>'>
</asp:DropDownList>
</EditItemTemplate>
<ItemTemplate>
<asp:Label ID="Label1" runat="server" Text='<%# Bind("Category") %>'></asp:Label>
</ItemTemplate>
That should work.