Fascinating conversation from beginning to end.
I have always argued that RS would neither resort to using "Harry" as his moniker, nor would LH feel particularly comfortable using it.
There are several arguments for the first: His need to utilize several names and identities interchangeably and often before assuming the mantle, whereas he was content to BE Remington Steele; his very pointed remark that Remington Steele was 'his good name' in Steele At It, and his anger when LH stated 'you don't have a name..."; his remorse that he should have to 'give the name back' in Steele Searching; his joy at receiving a passport bearing what he viewed as 'his name' in Steele Searching, again; and even his pride in holding up his PI credentials and saying a bit puffed chest 'Remington Steele.' Then, of course, there is the fact that the name ties him indelibly to LH, and the life he chose to build in LA, which he had never chosen to do before. Oh, and let's not forget, when Daniel refers to him as Harry, RS makes it very clear to him that his name IS Remington Steele in Blue Blooded Steele.
As for LH, Harry is a name tied to RS's past - and we all know how she feels about that. It would not roll easily off her tongue, and would, most likely, leave a distinct distaste. She is aware, from Daniel's old mouth, that Harry is a name RS was dubbed with from the 'bagful of names' he used when first he plucked him off the street. LH accepting RS as Remington Steele and calling him by Remington would be that last brick of defense she had left crumbling to ashes.
As for the bit about Daniel being RS's father - sorry, not drinking that Kool Aid. That storyline was as contrived as the entire Anthony Roselli CRAP. Canon, itself, tells us it is really NOT possible for Daniel to be his father.
BTW, whoever said the writers for season 5 had been the writers in all prior seasons is dead wrong. Actually, some of the flimsiest episodes with the least amount of Canon honored were written by one of those writers, who wrote once in Season 3, twice in Season 4 and had never bothered to learn the history of these two characters. To wit, at the end of Suburban Steele, LH utters, "The Remington Steele that walked into my life three years ago wouldn't care a fig what happened to my family." WRONG! RS immediately tried to ingratiate himself upon Abigail in Season 1, Episode 5; in Season 1, Episode 21 he is again spends time with Abigail; in Season 2's "Steele Sweet on You" after resolving the issue of who Donald is, he goes out of his way to get to know the Pipers. It's no coincidence, in my eyes, this crappola writer happened to be the head writer for the worst of the worst in Season 5 - and every episode in which Tony/Laura kiss or Laura seems to pant-pant after the man. Hello! We are talking LH here. Yes, she would be attracted to a man who has lied to her from the start, who has used her, abused her trust, blackmailed RS, not to mention sent him off to be possibly murdered? Puleeeeeeese.
As for the whole 'they hated one another' spiel, not buying THAT either. They were honest then and have been since, that there were tensions here and there generally spawning from PB's sudden shoot to stardom and SZ's frustrations at not receiving the same publicity. The gossip in the background seemed to far more center on Cassandra Harris's constant presence on the set and even her interference there. I suspect there was also some resentments/concerns re: SZ by Harris, as there is an article out there somewhere where PB candidly admits she was very jealous of his amorous scenes. Co-workers will not always get along and at times it can get UGLY, yes. But there are enough candids out there from the shooting of this series that show SZ and PB often joking around, smiling with one another, having fun.
Oh, and of course, PB freely admits directly after the series ended that he and SZ were both thoroughly pissed off for most of Season 5 - not at each other, but because they were both called away from projects they coveted in order to give their fans a horrible season 5, which he calls straight out - 'poxy'. As he pointed out in interview, RS had another solid season in it - one in which he would liked to have seen LH and RS settle down and even start discussing/having a family.
I know if I was called away from my future to serve up the pile of crap season 5 was, I would be tee-total pissed off too. :)