In the beginning, Elisa is incognito wearing the blue uniform. After Goliath awakens, Elsa arrests the villain in her traditional outfit. It's unlikely she stopped in the middle of a fight to change her clothes.
When Goliath greets the gargoyles by name, they respond (they are surprised he knows them), but if they had never met Elisa or befriended any other human, they would not have have had these names since Hudson would not have started the trend of taking names from New York's places after being informed of the river's name.
When Goliath searches the employment list for his job description (he stops by or around C. Berkeley), he is able to identify what he does, but he has no way of knowing what name he goes by in the alternate reality.