Formal:
* Engaged
* Appointed
* Hired
* Employed
* Contracted
* Retained
Informal:
* Got
* Asked
* Paid
* Ordered
* Created (for artwork specifically)
Specific:
* Assigned (for a task)
* Deployed (for military forces)
* Authored (for writing)
* Executed (for art)
* Designed (for a product)
Example:
* Original: The artist was commissioned to paint a portrait.
* Formal: The artist was engaged to paint a portrait.
* Informal: The artist was paid to paint a portrait.
Ultimately, the best word to use will depend on the specific situation and the desired tone.