Code needed for adding text onto current text every three rows down a column?

I have a list of names where the name is repeated 3 times and I need to add text after the second and the third repetition of the name. My Excel currently looks as following:
Morgan
Morgan
Morgan
Smith
Smith
Smith

I would like it to look like this:
Morgan
Morgan (ECI)
Morgan (HO)
Smith
Smith (ECI)
Smith (HO)

I'm still new to VBA and coding in general, I tried to write a code for this to add the (ECI) text to start and it didn't work. Any guidance on what I've done wrong and how to fix it would be greatly appreciated.

This is the code I tried to write.

Sub AddText_ECI()
Range("E3").Select
Do Until IsEmpty(ActiveCell)
ActiveCell = Range("E2").Offset(3, 0) + " (ECI)"
ActiveCell.Offset.Select
Loop
End Sub

Thanks for your response, that does work great. However, I tried to do it using code so I could try to start improving my VBA skills. So I was really hoping for some guidance on making this work with a VBA code not coding within a cell. I'm trying to use this as a learning opportunity rather than just using the simplest way to reach my goal, if that makes sense.

Thanks!

Maybe:

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Thank you so much this worked perfectly!

You're welcome. Glad to help out and thanks for the feedback and the rep.