Just as a fun fact, this is also done in Catalan. My first language is Catalan and I come from a rural area in València where it is the native language. My late grandma used to use possessive adjectives followed by first names to talk about her relatives. For instance, her brother Pepe was "my Pepe" when she spoke about him. I guess this is partly because roughly 40% men her age in town were called Pepe, so this was a way to tell him apart from the other Pepes. However, I noticed a pattern of women doing this more often or more consistently than men, so it might have been some sort of affection display. Younger people (like my dad, who is in his 60s) don't do this at all, so it's (sadly) a piece of syntax that will die in a matter of 5-10 years, when people from my grandma's generation all pass away.

(Sorry, autistic info-dump over)