Sumproduct: Determine The Number Of Unique Names In Column

I have 1500+customer names in column C7 of table. I'm looking for a SUMPRODUCT formula that achieves the following 2 logical goals. First, it needs to determine the number of unique names in column C7. It can't just count the rows because many customers appear multiple times in the range. So, I have been using the following formula and it works great:
=SUMPRODUCT(
((Table[C7]<>"")/COUNTIF(Table[C7],Table[C7]&"")))

Second, I'd like the formula to tell me how many of the unique names in C7 correspond to public companies. Column C8 of my table indicates whether or not a company is public ("Yes") or private ("No"). So, I've been using the following formula and it seems to deliver the right result:

=SUMPRODUCT(
((Table[C7]<>"")/COUNTIF(Table[C7],Table[C7]&""))
*
(COUNTIFS(Table[C7],Table[C7]&"",Table[C8],"Yes")>=1))

But the added COUNTIFS statement seems very unwieldy and indirect to me. Why do I have to examine every instance of a particular company's name when the answer could be determined by looking at any instance of the name -- after all, each company in C7 is either public or private, and has the same corresponding value in C8 (whether "Yes" or "No") everywhere that its name appears in C7!

So that's my first question: is there a clearer, more efficient way to achieve the same result? My second question has to do with toggling the public company test.
What if I create a special cell, say A1, that will always contain either the word "On" or "Off"........