General synonyms:
* Branch
* Affiliate
* Daughter company
* Dependent company
* Unit
* Division
* Component
* Arm
* Offshoot
More specific synonyms:
* Holding (when a company owns a controlling interest in another company)
* Associate company (when a company has a significant but not controlling interest in another company)
* Joint venture (when two or more companies share ownership and control of a company)
Informal synonyms:
* Spin-off
* Offshoot
* Side company
The best synonym to use will depend on the specific situation and the desired level of formality.