If it is your business, then you can file your return as such, regardless of which name the app might be in. However, it might be somewhat problematic if your husband receives a tax reporting statement with his name and SSN.
Regardless, you need to keep good records of your activities and expenses.
It is in his name so he would get the 1099 but I thought he could pay people working for him basically if self employed
There are several ways of possibly arranging a joint business, but if you have not taken any of those steps in advance, then, each of you are treated as having a separate self-employment business. You should file a schedule C, that reports your income and expenses, and calculates the net profit and self-employment tax, while your spouse should file a separate schedule C in their own name for their own business activities.
You need to keep accurate records of your mileage and your income. It would be far better for you to have a separate GrubHub account in your own name.
for this year, you will have to report your own income from your own records. If your husband also drives, he should report that income separately. If the 1099 is only issued in your spouse‘s name, you can still report income from your own accurate records, even if it is not on a 1099, while your husband will make an adjustment on his tax return to account for the fact that some of his 1099 income is actually being reported by you.