Formal/Medical:
* Assessment
* Evaluation
* Determination
* Identification
* Characterization
* Conclusion
* Findings
* Prognosis (if referring to the likely course of a condition)
Informal:
* Figure out
* Determine
* Pinpoint
* Identify
* Work out
* Unravel
Specific situations:
* Differential diagnosis: This describes the process of distinguishing between two or more conditions that share similar symptoms.
* Prognosis: This refers to the prediction of the likely course of a condition, often used in conjunction with a diagnosis.
The best synonym will depend on the specific context and the intended meaning.