Hi,
I think a normal premise behind making of a countable noun out of an uncountable noun is to make or distinguish into types. Can it be applied to proper nouns?
She found a way to help little Bobby.
Here, little isn't good enough to make Bobby into types, but this might do:
She found a cool Bobby sauntering along the road.
Here, cool might makes it cool enough to makes Bobby to wear many different personal hats.
Yes, I think you are starting to get a good grasp of this.
So, can we say for a proper noun like names, the nature of adjective can make a difference in making the name countable or uncountable? Maybe. And maybe it depends on the noun, too. I think it's a bit dangerous to generalize like this.
Can this only apply to names? How about other proper nouns? Hard to generalize.
Best wishes, Clive