It varies. Some require a modest retainer up front. Some will do an initial free design. Some will want a substantial retainer.

The best "shopping" that you can do isn't focused on the dollar. It's focused on finding the right person. Every designer has several cabinet lines at their disposal that they can quote you a very similar design in. I can do "white shaker" in any of the lines that I carry, and superficially, they can all look like the "same" kitchen. So, there's something for every person's price point, if that person will share what their budget might be up front.

If you find the person that you click with, and who gets your project, then you will have a successful renovation, no matter what your budget might be. If you merely shop price, then you are likely to not have a good experience with the project overall. The person is more important than the quote that you get. Let them show you around their showroom, and talk about their products. Ask questions. You should know at the end of the first meeting with them if you can work with them, before you ever get any design work from them.

What she said...
the only thing I'd add is understand that shopping for a person you are NOT shopping for a design, the right person can get you to the right design.