Launch Final Cut Pro, make a new project and name it with Automator
I don't have any version of Final Cut, but from the MacScripter search results it appears like at least the older versions weren't scriptable. Anyway, have you looked at its AppleScript dictionary (by e.g. dropping its icon on AppleScript Editor)?

Would it be possible to just copy a template file instead of creating a new project? If so, if you saved a script like this as /usr/bin/fcpp and ran chmod +x /usr/bin/fcpp, you could create a new project with fcpp Project name.

#!/bin/bash

mkdir -p ~/Projects/"$*"
cp -r ~/Documents/Test.fcpx ~/"Projects/$*/$*.fcpx"
open ~/"Projects/$*/$*.fcpx"