There is a tricky part now, because you will first modify the column "Weitere zugehörige Personen" by copying the data from "Nachname" and then probably want to clear the data from the column "Nachname". But your filter will change between these two steps as the column "Weitere zugehörige Personen" is no longer empty.
So I would first fix your current selection by either star or flag all the identified rows and use the corresponding star or flag facet.
Then use the transform dialog on column "Weitere zugehörige Personen" with the expression row.cells["Nachname"].value (no boolean functions and checks needed, as transformation respects your active filters).
Note that you could also use
row.cells.Nachname.valuebut I prefer the "quoted" variant as in my experience it is more robust against weird or special characters in column names.
This will copy the data from "Nachname" to "Weitere zugehörige Personen". You then can remove the data from the column "Nachname" via "Nachname => Edit cells => Transform => Common transforms => To empty string".