While there is no difference between "to commit suicide" and "to suicide"
. Note that "suicide" can also be used to refer to the subject of the suicide. So while you can say "He committed suicide" you could also say "He is a suicide".
 Although I would always use the first as it is, as has been said, far more common. )
As to why it is "committed" and not something else, I suspect it's one of two reasons.
The word, committed, has a finality associated with it. If you commit to something, you are making a pledge to do that thing and not go back on your pledge. Or, you may commit something to memory; the thought being that rather than it being a passing thing you have remembered, it is there for the long term.
Either that, or perhaps it is that "commited" is also often used in place of "perpetrated" in regard to crime. And until very recently (the 60's I think) in the U.K at least, suicide or attempted suicide was considered a crime. (Whether this was/is true in other parts of the world I don't know.)