Handed in notice, do I have to tell my current employer about my new role?

Posted 3rd May 2021
On Friday, I handed in my notice to my manager. But my manager, has stated that it is a requirement for them to know which company/role I am moving to incase there is a conflict of interest or me moving to a competitor or something along the lines.

I don't want them to know, but I also don't want a bad refernece.

Any advice guys?
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