I think Dan's pedant point is that even though the Escort engine was built by Hart, it was a Cosworth BDA type. The Lucas mechanical injection you mention is the same as used in period by most engine builders, nothing unique.
As said earlier, Hart went on to design and build a unique engine, the 420R, so that engine is rightly designated a Hart. Whoever built / builds a BDA, be it Wilcox, Richardson, Mass, Hart etc., the engine is still usually referred to as a BDA.
BUT obviously the owner can call the car whatever he wants- it's their car!
