Hi Suzanne,
First off, just a tip about posting to Geonet, you don't need to write that much text in the title of the question. There is a character limit, so your text will get cut off, which is what happened here. Just use the title as a general synopsis of what your question is about (in this case, something like "Field Alias not being retained after publishing to ArcGIS Online") and then put more details about the situation in the body of the question.
Even with the text cut off, I think I can understand what you're getting at. So the pop-up is showing correctly with field aliases used when you look at the visualization tab through the Item Details page, but not when you view the pop-up in a specific web map?
Best,
Katie
“The goal is not simply to ‘work hard, play hard.’ The goal is to make our work and our play indistinguishable.”
- Simon Sinek