On the Job Manager All report that is built in to Epicor, is there a way to add the customer name to it?

I’ve never heard of this report. Are you sure it’s native?

Regardless of what it is, the answer is probably ‘yes’. If it’s truly a native report, you will need to make a copy of the RDD and add it to a new report style.
If it’s not native, someone already did that bit and you just need to add the fields to the RRD/RDL.
(This is assuming you mean SSRS report when you say “report”)