Would the fact Harry gave "The Archive" a name, Ivy, and she took to it, mean that Harry knows her true name, a la Harry Blackstone Copperfield Dresden?
Assumptions:
Ivy is capable of being named.
Ivy took the name as part of her identity.
Not likely... but it still may be significant.
Ivy is only part of her identity. She was alive and active as the Archive for some time (admittedly, not long) before she met Harry. Ivy may be an accepted name, and how Dresden sees her, but it's not the entirety of who she is. So it's rather unlikely that just "Ivy" can be used as her true name; or if it is, like all magical mortals, she'd probably have to give it back to Harry, precisely and with intent, for Harry to use it that way, much like Harry gave pieces of his name away deliberately.
With a big however... this isn't even the only time such a thing happens, and it's implied Harry is dabbling in a way he doesn't understand.
Since Dresden actually prides himself on coming up with nicknames, here's a lengthy list of examples (later books have been spoiler marked)...
In Turn Coat, the naming of the island Demonreach is treated as significant by the spirit of the island itself. Later on in Skin Game, even being given a silly "first name" is given some serious thought by the island. Also in Turn Coat, the skinwalker is dubbed Shagnasty, and this is specifically called out as an attempt to lessen the fear surrounding the creature. In Ghost Story, Uriel, the archangel, is briefly called Uri, and this prompts an immediate and harsh reaction from the angel, a fairly scary one considering Uriel could simply unmake Harry with a thought if he got on his bad side. Harry backpedals but then immediately settles on Mr. Sunshine, which Uriel seems to grudgingly permit. In Cold Days, the Outsider creature is named Sharkface, long before it is learned what it actually is.
While Harry might not be actually creating true names - and probably wouldn't have a prayer, literally, of changing some of them - it's possible his constant habit of nicknaming can have a subtle effect on identity. After all, a lot of magic in this series operates on rules of perception. Anytime Harry tries to explain his spellwork he throws in how this element or that color fits the way he thinks. He also lampshades his own habit of nicknaming, and admits that he's humanizing and removing some of the mystique of these beings deliberately. If Harry is changing how people (even himself) view these entities, or changing how they see themselves, that's definitely significant, and the reaction of several of them to his habit seems to confirm he's doing something. Whether that's significant just for character development, or whether such a tenuous link could actually be useful magically speaking, to Harry or anyone else, remains to be seen.