Why Paul never used the word synagogue to describe the movement he inspired and chose ecclesia instead—the Greek word we translate as church.
The short answer is that he couldn’t use the word synagogue for a variety of legal and administrative reasons. Ecclesia was a better fit for their role as a para-synagogue organization within the Jewish umbrella.
There is a second option but not so strong as the first one. Paul thought of ecclesia as defining his concept of Messianic Judaism a restorative movement claiming back to the time of Ezra.
Jewish Christians
Christianity's Big Split from Judaism
The reasons and impact of Christianity’s separation from its Jewish parent.
Christianity started as a grass-roots Jewish movement that had its origins in the Galilee and Jerusalem regions.
There were two reasons that this offspring of a Jewish parent split: the destruction of Jerusalem, and their excommunication by Rabban Gamaliel II. This separation was distinct by the time of the Bar Kokhba revolt.
One must keep in mind that the separation was a gradual one. There were amicable relations between the two parties for centuries—so close that it caused competing interests.