I have added an note to a PDF file in Preview, and the yellow icon is covering up some text, but I can't move it away by dragging:
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You can move the note icon by clicking on the Text Selection tool or the Rectangular Selection tool (it looks like a square with dotted corners) and then clicking and dragging the icon to the area of your liking.
Make sure that you aren't in highlighting mode (click off the highlight tool at the top of the page) - you can't move the note around when you're highlighting.