**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.

 >! Lasciel's Shadow, gets nicknamed Lash, and in the end becomes an entity with it's own separate identity from Lasciel.  Uriel, the archangel, is also briefly nicknamed Uri