Enigmatic Variations 1501
Alternative Names by Kcit
NEW AMSTERDAM became NEW YORK CITY (across letter clashes) aka THE BIG APPLE (down letter clashes); COX is entered using four cells per letter, implying down letter clashes are chosen.
Sadly Kcit has chosen to not provide a setter’s blog for this site.
A full review of this puzzle can be seen over on fifteensquared.