ANAGRAM: Contemporary Composers, Letter Z

This time, we're starting from the end--the letter Z.

To wit, only 1 name (last, first) from our 6x6 grid, 3x2 region mini-Wordoku has been anagrammed.

You needn't worry, though. Unlike Sir Edward Elgar's great "Dorabella Cipher" or the punk glyph on the Phaistos Disc, this Classicalite Anagram is totally solvable.  

Can you, faithful Classicalites, decipher the name of him...or her?

Razes Hmm In
Raze Hmm Sin
Raze Hmm Ins
Ham Zen Rims
Harm Zen Ism
Harm Zen Mis
Marsh Zen Mi
Harms Zen Mi
Hams Zen Rim
Sham Zen Rim
Mash Zen Rim
Mar Zen Shim
Mar Zen Hims
Ram Zen Shim
Ram Zen Hims
Arm Zen Shim
Arm Zen Hims
Rams Zen Him
Arms Zen Him
Mars Zen Him
A Zen Hmm Sir 

Give up? Here, then, is the answer:

Zimmer, Hans (b. 1957)