Suicide: Abstract, technical and clinical, the term suicide, like the term homicide, is a euphemism which distances us from the stark gravity and emotional impact of the act.
Committed Suicide: When we say "committed suicide" we imply killing oneself constitutes a sin or crime, stigmatizing the act, the person who acts, and mental illness, if it seems likely to have played a role. We should avoid this term.
Died by Suicide: If I play linguist it seems to me that the preposition "by" here requires an object that implies some kind of method or action. For example, died by drowning or died by gunshot. Similarly one cannot say "died of suicide." Use of the word "of" requires a disease as in "died of cancer" or "died of malaria." Use of the word "from" might work for either as in "died from heat stroke" or "died from a fall." An actor might also follow the word by, as in suicide by cop. But is that really suicide?
Ultimately, however, I believe redundancy prevents "died by suicide" from working: the word suicide already includes and implies death.
Suicided: Technically the word may be used as a verb, but I find this awkward. Imagine saying, "She homicided the man accidentally." Perhaps the fact that homicide requires a specified object while suicide implies the object explains the difference. One cannot suicide anyone else, but homicide requires a victim. Which brings us to:
Victim of Suicide: Somehow "victim of homicide" is more comfortable, but constructions starting with "victim of his own" occur commonly, in keeping with our all too frequent self-defeating behaviors. Still, we think of victims as passive, and the idea of killing oneself implies intent.
Completed Suicide: This term belongs only in discussions contrasting it with "attempted" suicide. Otherwise the word "completed" is redundant. Imagine a "partial" suicide. Similarly:
Successful Suicide: Is this not a contradiction in terms? We generally view suicide as a failure, perhaps the ultimate failure, but of course the word "success" refers only to the act itself.
End His (Own) Life: Another euphemism, like:
End Her Life by Suicide: This construction suffers from the same problems as died by suicide, although perhaps somewhat less redundant. However, it does imply active intent.
End It All: Even more of a euphemism.
Kill Himself: My favorite, this phrase is stark and direct. It pulls no punches.
Take Your (Own) Life: Introduces the idea of taking something away, but too often the life is taken away from friends and family. Although one can certainly take someone else's life, even omitting the word "own," in the absence of another specified actor we generally understand this to imply suicide.
Die By Your Own Hand: Quaint.
Suicide by any other name is still suicide.