People have speculated he could have told her that he loved River Song however others think it more likely he told her his name. In Forest of the dead the Doctor said that there was only one time he could ever tell anyone his name, perhaps this could be when he believes he is dying. // He told her to tell River his name. His name unlocked the TaRDiS' telepathic interface to her. TaRDiS then told her everything she immediately needed to know. ( Supposition, of course -- but -- really! )
According to Alex Kingston, what Matt Smith whispered while they were shooting that scene was, "So, you used to look like Nina?", and she almost ruined the take by cracking up. But of course that's probably not what his character said in-universe. :)
Anyway, given that she replied, "Well, I'm sure she knows", his name doesn't seem to fit, while "Tell her that I love her" definitely does.
Ultimatly both could have been said and her responce was simily to the one of most importance to her.
I reckon he must have told her he loved her because Melody's reaction seems to fit with that.. If he'd told her his name then she would most likely have just been confused. Also, she sidestepped the question by Rory of what did he tell her.. If he told her his name then it seems likely she'd just say "his name" whereas it would be more difficult to tell her parents that he was in love with someone named River, who at that point she suspected to be herself..
Also, she seemed almost scared when she started to suspect that River was her, and knowing she's just killed someone who was in love with her seems to fit with that
"Anyway, given that she replied, "Well, I'm sure she knows", his name doesn't seem to fit, while "Tell her that I love her" definitely does"
I disagree with this - if he told her his name, and she assumed 'River Song' was the Doctors love/wife, whatever,
then she'd think it would be obvious for her to know his name...
He told her to look in his "eye" to see a miniture him in the Teselecta.
In the episode forest of the dead he said theres only one time he could tell someone his name, that is if hes dieing without being able to regernate;
"In the episode forest of the dead he said theres only one time he could tell someone his name, that is if hes dieing without being able to regernate"
I disagree with this because the only way he could tell someone his name is on the fields of trenzalore, on the fall of the 11th, that question will be asked, and silence will fall.
In "The Name of the Doctor" River states that she made the Doctor tell her his name. I don't think his name fits in this scene.
However, asking her to tell River Song that he loves her, or that he cares about her would make more sense. Also, remember in "Journey's End" that they more had the meta-crisis Doctor whisper that he loved her into her ear, rather than allow us to hear those words.