In the final episode of season 6 we see that Lyanna Stark is whispering something to Ned. What is she saying?
She probably says Jon, but there is no way to know for sure.
You may be thinking you failed to catch that line, but the producers made sure it is not audible after "his name is...". But "If Robert finds out, he'll kill him." points out to the child being a Targeryen. The face of the baby fading into adult Jon makes us believe he is Jon.
In the final episode of Season 7 (The Dragon and the Wolf), we get so see another flashback of this scene through Bran. This version makes it very clear what Lyanna says. She tell's Ned that her son's name is Aegon Targaryen.
"his name is Aegon, Aegon Targaryen"
I'll have to double check the exact phrasing later when I can rewatch the episode.
The scene purposefully makes Lyanna's comment inaudible to leave the suspense of the revelation of what she says. All the transcripts I could find also appear to omit this part:
LYANNA: Please. Listen to me, Ned.
LYANNA whispers in NED’s ear.
LYANNA: If Robert finds out, he’ll kill him, you know he will. You have to protect him. Promise me, Ned. Promise me.
Game of Thrones, Season 6 Episode 10, "The Winds of Winter"
However, as of Season 7 Episode 7, "The Dragon and the Wolf", this has now been answered.
His name is Aegon Targaryen. You have to protect him. Promise me, Ned.
Game of Thrones, Season 7 Episode 7, "The Dragon and the Wolf"