TheAuldGrump said:
Hmmm, serious answer to a facetious question time!
In most companies the head honcho and general wrangler is called president because they 'preside' over a board of directors in much the same fashion that the President of the United States 'presides' over Congress.
Conversely, a Prime Minister is the leader of a parliamentary system. Assuming that she/he is also the head of state (which isn't always the case, the Queen is the head of state in England and Canada) he* is first among equals, in a way. He is not elected or appointed separately from the legislature, he is elected to a seat in exactly the same way as a backbencher is. But he happens to be the leader of the party with control of the legislature, so he sets policy for his party and chairs the Privy Council, and has more influence than a backbencher, but technically has only a little bit more inherent power than any other member of parliament.
A president usually has powers above and beyond (or beside) the legislature or "board" that are inherent in the position of President, not leader of Party X.
So, Prime Minister wouldn't be appropriate for most business governance models. King or monarch, well, those are very specific hereditary and specifically political positions -- the term doesn't apply outside the political arena.
Generally, you name the jobs in your company so that people inside and outside the organization will know who they are dealing with, and who does what. If you call your "president" Archmage and your VPs Acolytes (e.g Acolyte of the Purse for the VP Financial Operations) well, customers, suppliers, colleagues and peers aren't going to know who is really in charge and it will just cause hassles when you are trying to convince a supplier that an Acolyte has the authority to sign binding operational contracts on behalf of the organization.
Cheers
*I use he, because Canada currently has a male PM. We've had a woman lead us, in the past, but I'm being lazy. No offense intended.