Ger [גֵּר] means simply a resident; as used in the Torah, it meant a foreigner which resided among another people or nation. Ger was never used of a person who changed their nationality to the nation among whom he or she resided. That this is correct can be understood from our father Avraham; as he was dwelling among the Cana’anites, he stated
גֵּר־וְתוֹשָׁ֥ב אָֽנֹכִ֖י עִמָּכֶ֑ם תְּנ֨וּ לִ֤י אֲחֻזַּת־קֶ֨בֶר֙ עִמָּכֶ֔ם וְאֶקְבְּרָ֥ה מֵתִ֖י מִלְּפָנָֽי׃
I am a ger and a toshav with you; give me a grave as a possession with you- that I may burry my dead before me. Genesis 23:4
It is clear that Avraham did not become a Cana’anite by dwelling among them- nor, for that matter, by receiving a possession among them.
A ger remains a ger- that is, a ger will always be known by the nationality in which he was born.