If a cathedral has to move in a diocese, is it normal to rename the parish?
The short answer is no. But indults do exist.
One would think that it would not be possible! After all Canon Law seems to make this quite clear.
Can. 1218 Each church is to have its own title which cannot be changed after the church has been dedicated.
Nevertheless I love ecclesiastical loopholes.
Once the church has been solemnly dedicated under the chosen title, this title cannot be changed. Canon Law 1218 is completely unambiguous about this. However, Omnis ecclesia titulum, February 10,1999, has ecclesiastical norms that may offer the possibility of changing the title of a dedicated church, but only for grave reasons and with a specific indult from the Apostolic See. I can not determine however, what might be a sufficiently grave reason, nor how disposed the Congregation would be to grant such an indult.
Still trying to locate a copy of Omnis ecclesia titulum from an Internet source.
It should be clearly understood that a church is, and always has been, dedicated to God: other dedications are annexed on an entirely different plane. Thus a church is dedicated to God in honour (for example) of the Blessed Virgin and the saints. A typical form is the following: "Deo sacrum in honorem deiparæ immaculatæ et SS. Joannis Baptistæ et Evangelistæ." In 1190 a collegiate church in Dublin was dedicated "to God, Our Blessed Lady, and St. Patrick". Sometimes out of several who are mentioned the patron is expressly designated, as in the dedication of a chaplainry in Arngask (Scotland) in 1527, "for the praise, glory, and honour of the indivisible Trinity, the most glorious Virgin and St. Columba, abbot, our patron of the parish". The celestial patronage here considered will be restricted in the first instance to churches and chapels. Patrons in different countries generally present a distinctly national colouring; but the principles which have governed the selection of names will be made apparent by the examination of a few instances. In comparing place with place, the rank or precedence of patrons should be kept in view. - Patron Saints
Thus it is quite possible to have St. Raphael as a principle patron saint with St. Bernard as a secondary patron also saint.
Here is an example of Bishop Salvatore Matano of Rochester invoking Omnis ecclesia titulum, in a name change of one of his parish churches.
Thus one could conclude that St. Bernard’s Parish could possibly become St. Raphael’s Cathedral! Good luck!