Exactly "icninin"means "one person" and "hitori" means alone. we don't use "ichinin" usually. meaning one person we use "hitori" How many people are you ? "hitori desu"or "hutari desu". However , "ichinin" is used in the word"ichinin-mae(一人前)".of course 一人称 too. ”一人前” means "a portion" or "a grown-up" In this case ,一人前 means "a portion".

Where have you seen the use of "ichinin"? That might answer your question. 一人(P); 独り(P); １人 【ひとり(P); いちにん(一人; １人)】 (n) (1) (esp. 一人) one person; (2) (ひとり only) (esp. 独り) alone; unmarried; solitary; (P)

Both have same meaning " one person", but I think there's a difference on the using. Like "hitori de" means "alone, by oneself", you can not read it as "ichinin de", right? I don't know hehehe... Will just wait and see what other people's answer about this. ^_^