In reading websters, it seems that 'hairstylist' is rather limiting. For styling the hair is simply that, either by blow-drying, roller-setting, curling iron, or plain old finger-styling.
There is, in fact, more design than styling, especially when dealing with color or dimensional work. There are a number of factors that should be included into the equation of hair design.

For example

It is a hairdesigner's professionalism that you are paying. Granted, they do perform a service. However, if you feel that you are not receive quality work, then you should seek out someone who believes that education is continuing.