The interactions of three people is more complex than the interactions of one person with himself. But the theory that my house contains three different residents still explains observations of my house much more simply than if you start with the assumption there’s only one resident. You accordingly cannot actually use Occam’s Razor to disfavor the theory that my house has three residents simply because the interactions of three people with each other are more complex than the interactions of one person with himself. Similarly, adding a cat to the three persons hypothesis actually improves the explanatory power of the model, even though you now have three sets of human-cat interactions added to the model; rejecting the cat on the basis of Occam’s Razor is also a failure.
Is a trinity more complex than a unitary godhead? In itself, sure. But if you’re trying to do something as notoriously convoluted as, say, theodicy, the question is, does the trinity provide extra explanatory power that reduces the overall complications?
And I strongly doubt anyone is both knowledgeable enough about theodicy and sufficiently rational and unbiased on the unity/trinity question to give a trustworthy answer on the question of which is the actual lesser hypothesis there. Especially since the obvious least hypothesis in theodicy is that there is no God at all and thus nothing to explain.
If you’re going to claim that a unitary godhead is favored by Occam’s Razor over a trinity, you actually need, among other things, a whole unitary-godhead theodicy. But if you actually worked one out, in order to have a rational opinion on the relative viability of the unitary and trinity theories, I’m going to wonder about your underlying rationality, given you wasted so much time on theodicy.
Of course simplicity is not the same thing as fitting the evidence. You only even start comparing simplicity after you have multiple hypotheses that actually fit the evidence. Then, and only then, can you properly apply Occam’s Razor. The hypotheses “Always comes up heads” and “always comes up tails” and “always lands on the edge” are all already on the reject pile when you’re trying to figure out the best theory for the existence of the “HTTHHT” sequence, and thus none of them get any points at all for being simple.
Indeed, if you’ve only got one hypothesis that fits, it’s still too soon to apply Occam’s Razor, except informally as a heuristic to encourage you to invent another hypothesis because your existing one looks excessively complicated. Only after you’ve got more than one hypothesis that fits the “HTTHHT” sequence can you actually use any formalization of Occam’s Razor to judge between those hypotheses.