First make the ComboBox.Text a two-way binding so that the view model property gets updated:
Text="{Binding Path=Name, UpdateSourceTrigger=LostFocus, Mode=TwoWay}"
With that in place, add a command to the ComboBox's LostFocus
event:
<ComboBox>
<i:Interaction.Triggers>
<i:EventTrigger EventName="LostFocus">
<cmd:EventToCommand Command="{Binding Source={StaticResource Locator},
Path=Main.AddNewActivityCommand}"
CommandParameter="{Binding ElementName=test,Path=Text}"
/>
</i:EventTrigger>
</i:Interaction.Triggers>
</ComboBox>
And finally, the "AddNewActivityCommand" should just add the new item (in the "Name" property) to the "AvailableActivities" collection.