If a male is born to a goy mother who converted after he was born, and a Levite father, following his own conversion can he be considered a Levite? And should his name include the name of his father or "Ben Avraham Aveinu"

Shalom, Since he was born to a non Jewish mother he would be considered not Jewish and would require aconversion. Therefore he would not be a Levi and would be called Ben Avraham Avinu to ensure that he was not mistakenly thought of as a Levi. Kol Tuv