Signed,
Sleepy or Dopey?

In your question, you have identified three points to think about. Here they are with a few comments:

• that your girlfriend may need more time to get over her last boyfriend — she is the only one who can answer that question.
• that you wonder if you are getting yourself into a position where you might get hurt. This is true with any relationship. The risk of getting hurt is always in the background, and human beings seem to keep choosing to take the risk when it comes to relationships.
• that you consider ignoring the whole thing. Unfortunately, ignoring the issue will resolve nothing. Since it seems to be bothering you enough to seek some advice, there isn't a very realistic chance of being able to ignore the situation, is there? Talking about your feelings and listening to hers can help you sort out the possible misunderstanding. You can be honest with your girlfriend and can ask the same of her.

These discussions can be challenging, especially since they deal with sensitive issues of jealousy and insecurity. A state-of-the-relationship discussion is probably the best option. Either it will ease your anxieties and reaffirm your girlfriend's commitment and interest in you, or it will allow you to make a clean break.

You can start by saying that perhaps this is a good time to (re-)assess your relationship. The two of you can set aside some time and choose a comfortable, even neutral place for this potentially uncomfortable conversation. Don't bring it up while in bed or on a date. You can be honest about your feelings of insecurity since the "name-calling" incident occurred, and about your feelings of caring for her. You can ask her to talk with you about her perspective and her feelings. Maybe your name starts with the same letter as her ex's name. Maybe it was a brain-freeze in the heat of passion. Maybe she was fantasizing about another person. Maybe she does need a little more time to get over her ex. Whatever the reason(s), and she may not even know why it happened, she can talk about her feelings for you. Either way, you will not know what's going on, or what your next steps might be, unless you talk with your girlfriend and tell her how you feel.