Suppose in a book there is a character named Alex, and he has a beard. There are no other Alexes mentioned. Which variant is correct?
1. "Hello," said bearded Alex.
2. "Hello," said the bearded Alex.
I lean towards the first variant, because it seems to me that we use "bearded" here just to remind the reader of that characteristic to make the mental image of the character more definite, and "Alex" itself does not need an article.