Yes, you can add tooltip text to DataGridTextColumn – just stylize it
<DataGridTextColumn Header="ScreenName" Binding="{Binding ScreenName}" >
<DataGridTextColumn.CellStyle>
<Style TargetType="DataGridCell">
<Setter Property="ToolTip" Value="{Binding Name}" />
</Style>
</DataGridTextColumn.CellStyle>
</DataGridTextColumn>