Someone said :
We also don't know the mom
explicitly, but it is.
What I mean is, it is obvious that the show is telling us that Lyanna is the child's Mother and that the child is Jon, but what the whole world seems to be forgetting is we do not "hear" the name of the father, we only hear that it is someone that if found out, would lead to the baby being killed.
Now, yes it does make sense that the father is Rheagar, but there is absolutely no guarantee at all that Rheagar is Jon's father.
The father could be any number of characters, including characters not involved in the storyline per se. Also, considering the popularity of the theory, it seem almost futile to "mute" Lyanna's message to Ed if Rheagar was indeed the father (since that's the most obvious possibility anyways).
That is, unless there is either a good reason (narrativly), or good dramatic cause (again narrativly) to leave the question open. Indeed there may not be good 'dramatic cause' to leave the question open; Rheagar being Jon's father would be an excellent development in the story anyways, obvious or not, but there is definitely good reason to leave the question open; it is simply not practical to assume there wouldn't have been anyone else in contact with Lyanna during a part of the story we've only seen/heard so far from character word of mouth.
There might be any number of as-yet-divulged affairs, rapings and secret meetings back in the time of Lyanna and the gang, that no one told anybody else about thus far.