The rename delay is tied to the setting for double-click speed in the Mouse Control Panel. The slower the double-click speed, the longer you wait for the Finder to enter edit mode after you click on a file name. However, if you hit the Return or Enter key after clicking on a name, you enter edit mode immediately (this is included for those who don't want to change their Finder). If you do, read on.
Use ResEdit to open CODE resource 11. At offset A28, you will find the value E388. You can substitute the following values to reduce the delay time:
1/2 normal delay, use 4E71 1/4 normal delay, use E288 1/8 normal delay, use E488.
Having changed the value here, you are still tied to the double-click speed. Other values are possible, but a better alternative may be to eliminate the delay completely. You can do this by going to offset A5A, where you will find the value 5DC0, and replacing it with 50C0. I've been using the latter patch myself for several weeks now without any apparent side effects.