I believe it's fear and nervousness exacerbated by memories of past episodes of stuttering or if you want "failures". You need to be able to calm yourself down first and foremost. Take in deep breaths before mentioning the names and slowly mention the names. I don't know if you already do it but mentioning the prefixes(Mr, Miss, Mrs etc) can also help ease you into the names. Better still you can write the names on a sheet or notepad and read from there. That way you don't have to look in the faces of the patients when mentioning their names which will reduce the anxiety and nervousness. Try these tips and see how it goes. Wish you the very best.