Can I select specific or same driver?
The Guru Take
Limos, taxi drivers, and some rideshare companies do offer this.
With Limo and taxi companies, you can request specific drivers upon calling ahead and making reservations. Whether the driver is available or can honor your request is obviously up to them.
Traditionally, as rideshares are considered "on-demand", you get the driver who is close to you at the time of the request, hence you could not specify a driver. However, recently, there are few rideshare companies who started to offer this as a feature.
Off the top of my head, Sitbaq and Wingz are two wonderful ridehail companies that offer this option.
On a side note, if you utilize more traditoinal carpool platforms, you can often get connected with the same drivers.