platonov,
The name hardly matters, does it? In asking about a text message that Amanda sent to Patrick, Amanda necessarily has Patrick's name suggested to her by the police (unless false memories, or general confusion get in the way of course

). Most of the talk on this has always seemed to me a silly game of trying to attribute first enunciating his name to either the police, or Amanda.
Who really cares, and why?
A more important question is surely - did the police know who the text was to before they asked her about it?
Another question would be - irrespective of who the text was to, how firmly did they have it set in their minds that the text related to the murder and that the recipient of the text was the killer?
Personally I am quite prepared to believe that the police thought they were onto something with the text, that they had caught Amanda in a lie and that her reason for lying was connected with the murder. Neither does it surprise me that they wouldn't have been immediately prepared to drop that belief on being presented, assuming they were, with what they later discovered was the true explanation. None of that seems to me to be improper.