How many times do people actually say Harry's name in all 8 movies?
I'll accept either
since just "Potter" could count for Lily and James as well.
Assuming the subtitles haven't missed any instances, Harry Potter's full name occurs 134 times in total.
The word "Harry" appears a grand total of 695 times.
The word "Potter" appears a grand total of 265 times.
Purely for the record, his name occurs in the books quite a lot too;
Also for the record, if your plan is to drink a shot of tequila each time his name is said, you'll be over the UK drink-driving limit within the first 30 minutes of the start of the first film and dead by the end of the second one.
Every Harry Potter Movie but only the words "Harry" and "Potter":
This might help. I would however advise viewer discretion, can lead to feeling of intense peevedness if viewed continuously.