As @Alesia has noted, only Mears is authorized to pickup on Disney property. Off Disney property you'll find other cab companies. I can't say I've had any experience with them so I won't offer any recommendations.
You can also arrange for car service. We used Tiffany Towncar. We were picked up at MCO and driven to Royal Pacific. The next day, we were picked up at Royal Pacific and driven to Coronado Springs. We made the arrangements before we left. Worked out really well.