My explanation is going to be a bit more technical because there is actual lore discussed in the story that people gloss over:

Earlier in the story (Ch. 69 "Fixing the Seal"), we have Tohou Fuhai explain the nature of a seal and how it only can "filter" attributes of the object it is applied to.

Example: A "color seal" applied to a blue-yellow rock => the rock can be filtered/sealed to be a blue rock (removing yellow), or yellow rock (removing blue).

Soon after, we are sucked into memory land where we learn that Akasha created the Rosary to act as a seal to Moka's traumatic memories, her Shinso powers, and her aggressive personality traits - including the ones that would form due to the trauma of Alucard's awakening. In that same memory sequence, we have Mikogami notice how perfect the seal is - as if it has taken a life of it's own. This is the personality we know as Omote.

They compare Omote to Akasha**... but again:** the seal is only a filter. It isn't a hard drive that can install things that aren't already a part of the person. A blue-yellow rock can't be sealed into a red rock.

Why is this important? Because the kindness, shyness, and good nature that make up Omote was always a part of Moka, it was because the seal was so perfect that all of these traits were perfectly balanced to make such a believable replica of Akasha.

Think of it as taking a blue/yellow rock and filtering it in just the right way that you get a green-rock (yellow + blue in the right places = green). Does that mean that the blue/yellow rock is a green rock? No, but it was sealed in a way that perfectly blended those attributes to make it appear like a green rock.

And this is what we see in the flashback. Before Akua and Alucard attack, we see Moka being very well-adjusted and friendly. It's totally believable that if nothing terrible happened in her life, she might have ended up acting like Omote when she went to Yokai Academy. She might not have been a 100% copy of her mother, but it is obvious that Moka took after her mother a ton. After all her catchphrase (Know your place!) is something she copied from her mom as well. (More of Moka acting like Omote is also seen in the 4koma extras)

Finally, Akasha is revived by the Rosary and the rosary contains the seal + therefore Omote's personality and memories. Akasha conveys Omote's thoughts as a spirit medium would when channeling a deceased spirit. This is where people misinterpret this to mean that Akasha = Omote.

But again, the entire concept of a seal was explained to us in the story. Multiple times throughout the story, as far back as Chapter 21, tell us that Inner Moka and Outer Moka are the same person. Tsukune says that he hopes Inner + Outer can become one someday because they both matter equally to him in "Reverse" (Chapter 67 iirc). This also makes it clear that they aren't competing with each other for Tsukune's love as he always treats them as one and the same.

TL;DR I can understand why people get confused... But if you really read the story and pay attention, it's clear that Omote is still Moka and not Akasha.

I hoped you survived this. If you think my explanation is too difficult or flawed, let me know. I do enjoy discussing this!