How to turn off click-to-rename feature in Finder
I don't know how to turn this off, but one way to deal with this is by tweaking the speed (i.e., duration) for double click and making it slower (i.e., longer duration) than what you currently have so that a single click does not quickly result in a rename action. The faster the double click setting, the more the likelihood of the rename action being triggered quickly.

You would have to experiment a bit to find the optimal double click duration while trying to not make it too slow for your use. You can set the double click duration by going to System Preferences > Mouse and adjusting the Double-Click slider.



On 10.9 the Double-Click options for Mouse and a trackpad have moved to the System Preferences > Accessibility  > Mouse &amp; Trackpad.