I don't think a Gentile becomes a Jew once a Gentile comes to the faith. In fact, later on in Ephesians 2 Paul writes:
2:19-22
"Consequently, you are no longer foreigners and strangers, but fellow citizens with Gods people and also members of his household, built on the foundation of the apostles and prophets, with Christ Jesus himself as the chief cornerstone. In him the whole building is joined together and rises to become a holy temple in the Lord. And in him you too are being built together to become a dwelling in which God lives by his Spirit.
Gentiles thus are not declared as Jews, but instead are fellow citizens. The adoption analogy works perfectly with this Scripture. We are not biological, but we are part of the family and reside under the same household. Through Yeshua, as Paul says, the two are brought together within the same household, yet Paul clearly made distinctions between Jew and Gentile is each of his writings.