Picaporte or Perilla in Puerto Rico.
Many Spanish-speakers in the US have never actually studied Spanish in school and some have learned the vocabulary typical of uneducated migrant farm workers spoken by their grandparents.
So it really isn't their fault for having a very limited vocabulary.
«Picaporte» according to my Ecuatorian friend is more like the kind of latch bolt devices installed in bathroom stalls here in the States to keep the panel door from opening, for example. I think «Perilla» is the most universal and can be said almost anywhere and be understood. If more context is needed then «Perilla de puerta» will work just fine.
Here is a Google Trends graph. It is not perfect, of course, but I think it helps understand the confusion. Keep in mind that "perilla" can have other meanings and that the line for "manija" in the graph is influenced by other countries' use of the word.