slkclassic is the name of their website (as well as the name of their modified SLK), but I reckon the company is actually A&A Custom Cars (see their Facebook or Youtube pages with the same name). Therefore I think the name should be A&A Custom Cars Barchetta 356.
I agree it's confusing, but I disagree about the marque name, as the 356 Barchetta appears in at least two car magazines as SLK Classics (where I discovered this machine) as well as their own design concept sketches. Even they can't seem to agree on their other names, as A&A Custom Cars is also written as AA and A+A! You got the point anyway, but to keep you happy I will add A+A (as it's most frequently written) to the subject heading as well!