How do I dispute an Apple Cash transaction sent to the wrong person

There no dispute process. As the name Apple Cash implies, you are sending cash to people.

You’re welcome to contact an Apple Cash Specialist at Green Dot Bank. Apple Cash is a service that’s administered by Green Dot Bank. Contact an Apple Cash Specialist at Green Dot Bank by calling (877)-233-8552 

https://applecash.greendot.com/termsconditions/

Apple Cash is a private transactions between 2 people. It is no different than giving someone on the street $100. You can cancel the transaction, but that is only possible before they have accepted it. There are no protections in a Cash transaction like you would find in a Credit Card purchase. It is recommended to only send Apple Cash to people you know. Apple makes note of that here:

Apple Cash person-to-person payments are like any other private transaction between two people, so only send and receive money with people you know.

Send and receive money with Apple Cash - Apple Support

If you would like to contact GreenDot bank that manages Apple Cash, you can do that here:

Contact Green Dot Bank by calling (877) 233-8552