So about this "Rebirth Potion"

Is it safe to assume that this is the equivalent of the Potion of Oblivion but just renamed by NA?

It is not a "Potion of Oblivion" as it does not reset exploration and current level to 1 upon use. Instead it simply makes the "rebirth" function available if it has been less than 6 days and 1 hour from your last rebirth. Meaning you will be able to choose a different talent or change gender like you would a normal rebirth.

Although publicly it is said you have to wait "7 days" to rebirth for free since the new beginnings update, your character can rebirth after 6 days and 1 hour has passed since your last rebirth.

Yea, a Rebirth Potion counts as a rebirth. A Potion of Oblivion does not count as a Rebirth and may only be used once per Rebirth. (KR has had both.) On another note, this potion should have a 24-hour cooldown I believe.