Seems RG3 is ALL IN with his new girlfriend ... 'cause he got her name TATTOOED ON HIS ARM!!
We're told the two hit up a tattoo parlor in Cleveland last month -- both got brand new ink on their forearms.
Robert's tat reads ... GRETE SADEIKO.
Grete is the 23-year-old Florida State track star who has apparently been dating the Browns QB for at least a month.
By the way, Griffin is STILL MARRIED to his wife, the mother of his child ... though they are recently separated.
As for Grete's tattoo -- hard to see what it says. Wonder if it's his name?