Mullier and other variants can't be correct. The second letter is clearly a capital A.
Here is a picture of it, and I have drawn what I think it is. The original is at the top and the redrawn version is at the bottom:
and itis possible, that the first L belongs to the A.
The small m is in front of the capital A, so I assume it is an abbreviation, in my case mensis (month), and then a month should follow, but there are al lot of other possibilities, without makron it could be: misce (mix) too
I would also see the symbol with the arrow as part of the L, i.e., a "h", but I also think that it is written too “modernly.”
There is a shadow at the top left, so it could be an r (could be).
This following "a" could be an ri, see the small inserted graphic on the right. But of course, that is also uncertain.
In my opinion, it is relatively clear that the apostrophe at the end of the word is an apostrophe; it is written like a small “v.” This makes it rather unlikely that it can be attributed to the letter before it.