This is one of those Easter eggs Marvel put in their movies. Morgan Stark happens to be Tony's cousin and enemy in comics, but they named his future son. It seems that Marvel wants to try something new other than comics and release new movies with new characters in MCU (though no confirmation yet). This might be explained in future (possibly with release of Infinity War sequel)
In one interview with Gwyneth Paltrow (who plays Pepper Potts), she told about the future relationship of her character with Tony Stark. (might be a spoiler for upcoming movie. Ye be warned)
“Pepper and Tony have had a really long journey together,” Paltrow said in the interview. “She obviously starts as his dutiful assistant, and then the relationship evolves, and now this decade later they’re married, and they have a child. Their relationship has evolved in all of the ways that great romances evolve.”
Though, Pepper Potts denies the dream of Tony about having a child and naming him Morgan, but this statement suggests that there might be something to his dream after all. Morgan Stark will possibly be his son in MCU and then made one or more movies about him.
From the same article (with my edits and emphasis),
If there’s a baby on the way that could confirm some potential theories about where the MCU is headed in the future. At the very least, it would provide Tony a good reason to retire from superheroing, which seems likely since Downey’s MCU contract ends with “Avengers 4” in 2019. If he hangs up the Iron Man suit to become a family man, that would allow Marvel to keep Tony around for occasional cameos and assistance in the MCU — and that feels more likely than killing the character off.