The gemara (Yoma 75a) writes that the more righteous someone was, the closer to them the manna would fall.
Given that there were two million people encamped in close proximity, how did someone know which portion was supposed to be his?
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The actual language there in Yoma 75 is, "The righteous, it fell by the door of their houses." That would be a good sign it was for them.
Either way, I don't know if there was a concept of "his" or "someone else's" until one picked it up. It was there for the taking; you'd walk until you found some to gather; you'd gather until your measure was filled. The wicked just didn't seem to find much until they had walked a greater distance.