General:
* Initials
* Cipher
* Mark
* Symbol
* Design
* Embellishment
More specific:
* Interlaced initials (if the monogram is specifically intertwined)
* Crest (if the monogram is a family or organizational emblem)
* Logotype (if the monogram is used as a brand identifier)
The best synonym will depend on the specific context in which you are using the word.