Most priests do not know that they have a canonical right to stop naming Bergoglio in the Canon of the Mass. They think wrongly that to do so would either be outside of their authority or would involve an act of schism. That it is not schism nor a sin, is proven thus:
Here is the canonical argument
First, a validly elected Pope must be named in the Canon of the Mass as a sign of communion. This is by tradition and liturgical law.
Second: Pope Benedict XVI was validly elected Roman Pontiff on April 19, 2005 A. D., just three days after his 78th birthday.
This is a dogmatic fact, which cannot be denied.
No validly elected pope’s name must be omitted from the Canon of the Mass during his lifetime, or before he validly resigns.
Third: Pope Benedict XVI did not resign on Feb. 11, 2013, he merely retired from the active ministry, as he himself said on Feb. 28, 2013 in his final Allocution (see other evidence here). For extensive canonical information about this see ppbxvi.org.
Fourth: That Pope Benedict XVI did validly resign was the falsehood which emanated from the Desk of Cardinal Sodano. (See explanation here)
Now just as Cardinal Sodano should have acted, is how all priest should act. Namely,
In accord with Canon 40, Priests who are to say mass hold a munus which is merely executory, in regard to whom to name at Mass in the Canon as Pope. This is because they do not decide on their own authority who is the pope and who is not the pope. They follow the command of a superior. That superior is above all the Pope.
If a pope therefore does not renounce his office in accord with canon 332 §2, because he renounces his ministerium instead, that renunciation has no canonical effect, because there is no canon in the Church’s laws which regard the renunciation of ministries.
Therefore, in accord with canon 40 and 41 A PRIEST IS FORBIDDEN to alter the name of the Pope in the Canon of the Mass. He cannot act on the basis of the declaration of Non Solum Propter in the same illegal manner Cardinal Sodano did. To do so would be to collaborate in his grave crime, deceive the faithful and enter into de facto schism with Pope Benedict. (see that article for a greater explanation of the crime and moral offence)
Therefore, a priest must continue to name Benedict in the Canon of the Mass.
Therefore, a priest must cease and desist naming Francis as soon as he recognizes the validity of this canonical argument.
(This argument is not that of the Editor of this Blog, who has merely expanded it for a fuller explanation — There are already a great number of priests who do not name Francis, but name Benedict instead, some openly, some secretly, some by saying for the Holy Father, without a specific name. God bless and strengthen and multiply these priests!)
NOTE BENE: There is a lot of misinformation out there, from Vatican News, which falsifies things attributed to Pope Benedict. Here is one glaring case from last June, WHEN Vatican News claimed that Pope Benedict said, “There is only one Pope, and he is Francis”, which never actually happened. Click the links in the Twitter Card, below, for more on this.