Wanting to leave my job and I don't know if I should include its contact info in the work experience on applications

I am trying to leave my job at a deli because I'm getting virtually no hours. Should I include its phone number and my boss' name when I add it as work experience? I don't want to tell him I'm applying elsewhere, but at the same time it's only my second job and I left my first one because my boss there was the worst on the planet when it came to how she treated everyone, so if I don't include my current job's info, the one I'm applying to will have no references to inquire about me. It's Ross, so I'd imagine it's not extremely competitive to get hired there though.

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