In The Godfather II, before gunmen try and kill him, when Michael enters his bedroom and Kay wakes up, we can see that bed linen has a monogram "mCf" on it.
My search shows that it could be standing for:
But I can't find any source providing reliable and undeniable evidence for a definitive answer.
What does the MCF monogram stand for?
This is how monograms work. The center initial is the surname, and the first initial is the first name, and the last initial is the middle name.
Source: https://en.wikipedia.org/wiki/Monogram, see Individual Monograms:
A basic 3-letter monogram has the initial of the individual's last name (surname) set larger, or with some special treatment in the center, while the first name initial appears to the left of it and the middle name initial appears to the right of it. There is a difference in how this is written for men and women. For example, if the individual's name is Mary Ann Jones, and Jones is the surname, then the arrangement of letters would be thus: MJA, with the surname initial set larger in the center, the M for Mary to the left and the A for Ann to the right.
