I need to schedule a ride for a specific time in order to arrive at doctors ...
The Guru Take
Try a local taxi or black car company
If you are looking to use Uber, Lyft or another mainstream rideshare company, there is currently no way through these apps that you can request the same driver for every trip. However, if you take a taxi or black car service you can request the same driver for multiple trips. Overall, there isn't much benefit to getting the same driver for multiple trips except comfort level with your driver. If this is something that is important to you then I would look into using a taxi or black car company.
Also it is important to note that Uber and Lyft only have scheduled rides available in a few cities, to learn more about scheduled rides and if they are available in your city check out this previous Guru answer: https://ride.guru/lounge/p/can-i-reserve-a-car-for-future-date
More useful topics
To add on to Lilly's response, here are a few good articles: