Q. When making a mi sheverach for a sick person who is a cohen, do you mention hacohen after his name or after his mother's name?
A. Birkey Yosef (Y.D. 240: 4) writes that when praying on behalf of one's father or Rebbe, he should omit mentioning titles of honor. As Shlomo said when talking to Hashem; "David my father" and Elisha expressed: "the G-d of Eliahu". The reason is that in front of Hashem we can only be humble. Uriah, he adds, was considered rebellious when he mentioned; "my master Yoav" in the presence of King David. A similar position is quoted in Minchas Chinuch (257: 12) in the name of Maavar Yabok.
Horav Shlomo Miler's Shlit"a opinion is that you don't have to mention in a Mi Sheverach the fact that the sick individual, is a cohen or levy.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit"a