What a student sees on their calendar when they login in is:
1) All lessons they are a participant in
2) All “global” events that have no participants
3) All events that are open for registration
The students will not see any events that other students are scheduled for, such as other students’ private lessons. If there is an event they’re seeing that has another student’s name on it, check the event to make sure that the event has the correct student set as a participant. It could be that you titled the event with a student’s name, but didn’t actually add them to the event as a participant. You can add a student as a participant by editing the lesson and:
1) Type the name of the student in the “Student(s)” field, then click the name.
2) Click “Show all students”, check the name(s) you want, and click “Add selected”
When a student is a participant, their names will show below the Student(s) field with a [Remove] link next to them.