Jobbers in small fields- would it be appropriate to mention my new place of employment in my rejection thank you letter?

My field is <very small>, and I interviewed for similar positions at two places who will likely have extensive interactions together (county gov and private transport). One hired me, one rejected. In my thank you letter to the rejecting manager, should i mention where I was hired? The chances of me meeting him specifically in the next year in a professional context is about 75%.

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