Hey Philipp, welcome to the Community!
The out-of-box customer feedback/satisfaction surveys don't support changing the stars to thumbs-up/down. I've looked through the Marketplace and the closest I've found to customizing the feedback like that is the Surveys for Jira app, which is actually more granular rather than simplifying the feedback to two choices. I think it's worth having a look at the surveys solutions on the Marketplace to spark some ideas for ways you might want to do feedback, based on pre-existing solutions.
It's unlikely that customization for thumbs instead of stars will be added to Jira Service Desk itself. But if this is something your company is very interested in, it might be worth reaching out to an Atlassian Partner to see about creating an app to meet your needs.
Cheers,
Daniel
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