Modify your SqlDatasource as
<asp:SqlDataSource ID="SqlDataSource" runat="server" ConnectionString="<%$ ConnectionStrings:ConnectionString %>" DeleteCommand="DELETE FROM [Users] WHERE [Id] = @Id" InsertCommand="INSERT INTO [Users] ([Id], [Name], [LastName],) VALUES (@Id, @Name, @LastName,)" SelectCommand="SELECT * FROM [Users]" FilterExpression="Name LIKE '%{0}%' UpdateCommand="UPDATE [Users] SET [Name] = @Name, [LastName] = @LastName, WHERE [Id] = @Id">
<DeleteParameters>
<asp:Parameter Name="Id" Type="Int32" />
</DeleteParameters>
<InsertParameters>
<asp:Parameter Name="Id" Type="Int32" />
<asp:Parameter Name="Name" Type="String" />
<asp:Parameter Name="LastName" Type="String" />
</InsertParameters>
<UpdateParameters>
<asp:Parameter Name="Name" Type="String" />
<asp:Parameter Name="LastName" Type="String" />
</UpdateParameters>
<FilterParameters>
<asp:ControlParameter ControlID="txtSearch" PropertyName="Text" DefaultValue="%" />
</FilterParameters>
</asp:SqlDataSource>
Add
FilterExpression="Name LIKE '%{0}%'
AND
<FilterParameters>
<asp:ControlParameter ControlID="txtSearch" PropertyName="Text" DefaultValue="%" />
</FilterParameters>
Please replace that the txtSearch I used for ControlID with the ID of your textbox which is used for search.