It's not useful to confront your parent at the time of the name-calling when they're upset. Pointing it out at that moment will only make them hostile, defensive, and unable to absorb the emotion behind what you're communicating. Wait until you're both in a relaxed mood to bring up the matter.
If your parent is especially sensitive to criticism, bring up the subject in a general way. Share the latest research in neuroscience that shows how verbal abuse can alter the brain's structure and lead to long-term problems. Have them recall a time from their childhood when they were called a name and ask how it made them feel.
If you choose to talk about your parent's specific behavior, use “I messages” to diffuse the situation. For example, say: “I feel hurt/sad/betrayed when you say that.” Don't say it in an accusatory way: “You always call me that when you're mad and you're causing me so much pain!” When people think a finger is being pointed at them, they tend to shut down and stop listening.
If your attempts are unsuccessful, turn to a trusted family member or family friend and ask them to discuss it with your parents. I'm glad that you're being pro-active and looking out for your own well-being. I know how miserable it is to grow up in a home with parental name-calling.