There is a Thomas Johnson, age 22, born in Greece, not naturalized, living in Washington state in the 1920 census for Gray's Harbor, working as a laborer in a sawmill. Could this be him? There are a William Vassio and a Sam and John Pappas, all born in Greece, living in the same boarding house at the same time.
Don't discount this Johnson based on the age or location alone, as very often workers said they were younger to show they were healthy and young enough to be hired, or said they were older, to show they had experience in their field. And, by 1920, he could have come back from Alaska, or worked in Washington temporarily, then returned at a later date.
Sometimes the incorrect age is because they really didn't know the exact year--mostly the greeks celebrated saint or name days instead, and if the family they came from were farmers in small village areas, exact years weren't known to them, nor did they need to know. Most didn't have watches or clocks, and lived by the church calendars or clocks, and guessed when their birthdates were, and knew by the sermon the priest gave at a certain time of year, that it was time to plant or harvest or whatever, and that was close enough for them!
I would bet, like my Rocco Rosello, who sometimes used the name Rick Russell when he worked in the mines, that your ancestor used Thomas Johnson for work and when finding a place to live, and to establish an account at stores to trade for groceries, etc, to avoid outright discrimination toward Greeks, but retained his legal name of Athanasias Ioannou all his life.
Let me know if this is him and I'll do more follow-up if I can.