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So Oedipus comes along, gets into a fight with a stranger (his father, unknown to him), and kills his father. Depending on the telling, either the killing was intentional, or it was in self-defense; let's assume the former. If Oedipus intended to kill Laius, and Laius is Oedipus' father, but Oedipus didn't know that Laius was his father, did Oedipus intend to kill his father?

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Your question raises what is known as the "de dicto/de re" distinction. Rather than give a formal explanation of that (for which, have a look at the Stanford Encyclopedia of Philosophy), I'll try to put an answer without using the distinction explicitly.

One way we can think about intentions is to think that an intention is at least partly contituted by the specific content in which the intention would be expressed. Hence, when Oedipus killed the man where three roads met, his intention was not to "kill his father" (or, for that matter, to "kill Laius"), but to "kill the SOB who has the gall to push me--the crown prince of Corinth--aside"). In other words, if you asked Oedipus, "What is your intention?" he would surely not sincerely reply in terms off anything having to do with his father. On the other hand, it is also true that there is another sense in which he intended to kill his father, since he intended to kill that man, and that man = his father. But I think if we were reporting his intentions, it would be somewhat misleading to describe his actions as "intended to kill his father," and so the first sense is the one that would be more appropriate (for example, if we were testifying at a trial).

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