In telephone conversations, pauses are less acceptable. You are expected to continuously keep the conversation going. Also, you are unable to use non-verbal communication. Saying one's name. However, I haven't found any studies showing that stuttering is more likely on words starting with the initial sound of your name.
Timing is critical to jokes, so there is more anxiety about saying a punchline fast.
Saying something important or meaningful. Stuttering is less likely when, for example, reading a list of numbers. If you believe a listener is hard to talk to or critical. You are likely to stutter less with someone you perceive as easy-going or understanding. Talking to an authority figure.