If people are coming to you personally because they like you, I would be very careful with the people you employ.
My suggestions:
1. Get people who can do the admin or other time consuming activities to free up more time for you to do the instruction.
2. Include different instructions throughout the series of lessons. I had private language lessons at a stage and before the course started I was interviewed to ask what my specific needs were. They then found the best teachers who would be able to help me with those elements. In my case, I ended up having one teacher who was really good with conversation, one that was really good with grammar and another who was really good with pronunciation. About 80% time was with my favorite instructor, the other 20% was an odd lesson with the one guy and then the other.
I found this was super beneficial to my learning as each teacher had a different strength and perspective so I felt I was getting more than what I would have if I only had one instructor.
In terms of actual branding, maybe do something easy like branded clothes or branding the car you use for driving lessons if it's not the clients'. Something that is associated with the personal space, not the external factors like a website or email message.
Good luck!