Totally normal. Wait it out. Don't force her to be with people she isn't used to. If, when she hears their name, she thinks you're going to leave her with them (babysitter, grandparents, neighbor), sometimes that's enough to set her off. If it's a babysitter, you need to figure out if something bad happened (she got spanked or yelled at) or if she just gets upset about parents going out for a while. Separation anxiety (along with the clinging) is very common and there are different ways to handle it. Talk to the pediatrician and also ask the children's librarian for some helpful books on child development so you can learn about these not-so-pleasant phases in children.