General synonyms:
* Quiet
* Shy
* Withdrawn
* Unassuming
* Introverted
* Reticent
* Discreet
* Cautious
* Moderate
* Self-contained
* Inhibited
Synonyms emphasizing a formal or polite demeanor:
* Polite
* Formal
* Courteous
* Diplomatic
* Tactful
* Reserved (this word itself can imply politeness and formality)
Synonyms emphasizing holding back or withholding:
* Hesitant
* Reluctant
* Unwilling
* Holding back
* Withholding
Synonyms emphasizing a specific area:
* Tight-lipped (for secrets)
* Conscientious (for a person who is careful and thorough)
* Conservative (for a person who is traditional or cautious)
The best synonym for you will depend on the specific context and nuance you want to convey.