What API or procedure can retrieve the ICC Profile Name associated with an ICC-Based element?

The ICC profile name is part of the ICC stream embedded within the PDF document.

The stream following the /ICCBased key is the ICC itself [ /ICCBased stream ]. You need to convert the stream to an ACProfile withACMakeBufferProfile() and then use the ACProfileDescription() API to get the description. An AC_String is returned fromACProfileDescription(), so you will need to use one of the ACString functions to convert it to a usable string.