On the traditional understanding of Christ's Incarnation, Christ has two minds—a human mind and a divine mind—even though he is one person. The two minds have different mental states. In his divine mind, which he has in common with the Father and the Holy Spirit, Christ is omniscient. In his human mind, he is not. There are things that he knows with his divine mind which he does not even believe with his human being, because there are thoughts conceptually beyond the ability of the human mind to think. Yet how could one have two incompatible collections of mental contents like that, and yet be one person? Likewise, Christ divinely wills certain things, say that all reality continue to exist, which he presumably does not will humanly.
But suppose that the past is real—i.e., that either eternalism or growing block is true. Then I, too, am a person with incompatible collections of mental contents. At age 2, I did not even have the concepts needed to grasp the Pythagorean Theorem. Now I know the Theorem to be true. Yet it is the very same person we are talking about here. So the very same person has two incompatible collections of mental states.
But there seems to be a difference. I don't know the Pythagorean theorem at age 2, but I know the Pythagorean theorem at age 40. There is no problem here. But Christ at the same time knows and doesn't know some propositions.
Actually, though, it's not clear that it makes sense to say that Christ at the same time knows and doesn't know some propositions. In his divine nature, Christ is timeless. So perhaps we should say that Christ at age 30 doesn't know p, but Christ timelessly (or "at eternity") knows p.
But that's not exactly my point. The point I want to make is a little subtler and would hold even if God was in time rather than being timeless: the adverbial modifiers "at age 2" and "at age 40" work rather like the modifiers "as human" and "as God". Just as there is no contradiction between my knowing p at age 40 and not knowing p at age 2 (or vice versa), there is no contradiction between Christ's knowing p as God and not knowing it as human.
There is a sense in which the succession of time multiplies our wills and minds: we pursue and believe different things at different times. While I don't want to say that we have literally different wills and minds at different times, the diachronic distribution of our pursuits and beliefs shows that personal identity does not require any strong unity of apperception. At most, according to some theorists, there need to be some interconnections, like those of memory. And other theorists—the ones who are right!—don't even think connections of memory are needed for personal identity.
The analogy between times (in our case) and natures (in the case of Christ) is of course only an analogy. But I think it is potentially a fruitful and underexplored one. Notice that the analogy extends beyond the mental life. Just as Christ is both omnipotent (as God) and weak (as a man), I am both relatively strong (now) and helpless (in infancy).
How well the analogy runs will depend on the theory of persistence over time that one is thinking about. I am inclined to either endurantism or stageless worm theory, so those are the theories on which the above intuitions are based. But one will get a different picture—perhaps no longer orthodox—if one bases the analogy on perdurantism.