Answer:
Jekyll believes that, because of his secret, he must avoid seeing his friends.
Explanation:
In the passage Jekyll says, "I have brought on myself a punishment and a danger that I cannot name." Since he is not willing to name the punishment and danger, it remains a secret. Because of this he decides that he needs to "lead a life of extreme seclusion." This means that not only will he isolate himself from Dr. Lanyon but also from his other friends.