My friend, colleague and prolific commenter David has on my website suggested that "doorman" is an obsolete comment. I presume he means it is inappropriate because of being gender biased.
I am usually very careful about such things, and was putting "s/he" in documents in the early 1980s when I was a "headmaster" (rather than a headmistress).
But I do not see a problem with doorman. In the unlikely situation of a woman taking on the role (and although I know one or two who could, I doubt that hardly any exist) David can call them "doorwomen" - but please, NOT "doorperson".