Here is the pattern that you are looking for:

[:LetterSpace:]*([:Dot:][:Letter|Space:]*)*

Regex Pattern:

^([a-zA-Z ]+(?:\.[a-zA-Z ]*)*)$

OR, because you are matching only, not capturing:

^[a-zA-Z ]+(\.[a-zA-Z ]*)*$

Regex Demo: https://regex101.com/r/Cha5FW/1