If you're the type of person who likes to keep track of their car's maintenance history, then yes, you should hang on to your oil change receipts. That way, you'll have a record of when the oil was last changed and can easily reference it the next time you need to get your oil changed. Plus, if there are ever any issues with your car down the line, having these receipts could be helpful in diagnosing the problem.
However, if you don't care about keeping track of your car's maintenance history or don't think you'll need those receipts for any other reason, then there's no need to save them. You can just throw them away after your oil change is complete.