Not officially, but there are a couple of retronyms.

Larry Wall originally wanted to call it "Pearl", but found there was already a language by that name, so he shortened it to "Perl".

The name is sometimes expanded as "Practical Extraction and Report Language", or as "Pathologically Eclectic Rubbish Lister" (Larry Wall's own phrase, mentioned in the Perl man page).

But yes, "Perl", not "PERL", is the correct name for the language.

(Ada, which was named after a person, has had the same problem, though as far as I know there isn't even a retronym for Ada.)