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If a school does not ask for your name and LSAC # on the top of your personal statement and the only written document you send is your personal statement (besides your resume which naturally has your name on it), would submitting your PS with a blank header be looked upon negatively by the adcomms?

i dont think so. If they dont ask for it, it wont hurt you. ( some admissions people dont even print the application off- as a way to save paper)
If you want to be safe, do it anyways, but dont worry about re submitting.

I don't think it would hurt you if you leave it off, but it certainly won't hurt to have it. I personally always put a header with my name, LSAC # and page # on it, just in case someone messes up or something gets dropped or shuffled.

Its about presentation and professional work. It is something that adcoms notice. I think not having it doesn't really hurt you, but having it makes you stand out as someone more mature, professional and ready for the world and work force.