Family Members Names
Again, for the sake of comparison, I'll show the examples in Portuguese:

Avô (Grandfather), Bisavô (Great-grandfather), Trisavô, Tetravô, Pentavô, Hexavô and so on.
We keep ordering with the greek numbers the older relatives.
Or, in a informal and funny way of speaking, we would change 'trisavô' for 'tataravô' (a corruption of 'tetravô', actually) and just add 'tatara-' for every older generation. So, 'tataratataravô', tataratataratataravô', like a machine gun, a test of our tongues' skill as well.

How to say that in English? We should add 'Great-' for every older generation (e.g. Great-great-grandfather)?

Question

Family Members Names
Again, for the sake of comparison, I'll show the examples in Portuguese:

Avô (Grandfather), Bisavô (Great-grandfather), Trisavô, Tetravô, Pentavô, Hexavô and so on.
We keep ordering with the greek numbers the older relatives.
Or, in a informal and funny way of speaking, we would change 'trisavô' for 'tataravô' (a corruption of 'tetravô', actually) and just add 'tatara-' for every older generation. So, 'tataratataravô', tataratataratataravô', like a machine gun, a test of our tongues' skill as well.

How to say that in English? We should add 'Great-' for every older generation (e.g. Great-great-grandfather)?

Answer

Yes, it's "great-great-great-" if you like, or "fifth-great, sixth-great," etc., as in Portuguese.

We also say, "My grandfather's grandfather,", etc., or "my grandfather seven generations back on my mother's side", etc.