Is it OK to ask an individual to change payment to me regarding money owed due to a car accident?

Question Details: A co-worker and I were leaving work and he backed into me and said that he'd pay for it. So I got a body shop estimate and it's for $960. However, I have someone telling me they would could do it on the side and do it much cheaper. The co-worker gave me the check for the full amount in the body shop's name. Would it be wrong to ask to change it to my name?

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