Generally speaking, the surrogate gets to choose the obstetric medical provider. They will often choose the same as previous pregnancies because they already have an existing relationship with them.
However, another provider may be chosen If the surrogate or intended parents have any specific requests, such as delivery at a hospital with a high-level NICU. It is important to talk about these items during the application and matching process.
The Gestational Carrier Agreement will usually address who will provide medical care during the pregnancy and where the surrogate plans to deliver.