Some pagan ideas were incorporated into the church when Constantine married the church to the state.
The name Pontiff was originally the name of the High Pagan priest in Rome.
The basilica and church architecture was taken from Imperial Rome.
The Diocese was an Imperial Roman administrative unit.
Constantine was overall very bad for the church.
Inculturation takes place in every religion and religious community. At the most basic level this includes words, names, and attire. When Latin speakers needed to name the office of the pope they used and existing Latin word for their highest priest. The basilicas were existing repurposed governmental and administrative structures. They were changed because the focal point of the buildings in Roman use was the center of the building. When converted to Catholic use the focal point, the altar was placed at one end of the building.
The diocese was not an Imperial Roman administrative unit, its origin, along with the word diocese was Greek (διοίκησις), meaning "administration" and was developed by Alexander to manage his empire.
Peace be with you.