Can an individual who gives evidence during a workplace investigation request anonymity? 

If the witness asks to remain anonymous, you should explore the reason for this request and any underlying motive. There are a number of reasons why someone may request anonymity: they may genuinely be fearful of violence or other repercussions or simply may not want to be seen as a 'snitch'. You should always establish the reason for any reluctance as well as consider the possibility that the employee or witness may have reason to fabricate, or otherwise embellish, the evidence they give.

Consider taking steps to protect the witness's identity, such as redacting their evidence to remove their name and any other information that may identify them, if possible (however it can often be easy