If you want to be technical, you can call it Eastern Nagari. In practice, the name “Bengali–Assamese script” doesn’t seem to be used outside of Wikipedia and adjacent projects: it’s overwhelmingly called the Bengali script, with Assamese materials calling it the Assamese script. The fact that there are almost 20× as many speakers of Bengali as there are of Assamese probably contributes to this. (There’s also Manipuri, but it’s smaller still.) I find references to some ISO decision from June 2018 to recommend renaming the Bengali script to Bengali/Assamese script in Unicode (less than they were asking for, which was separate encoding due to some pronunciation differences), but I can’t see that this has happened. But I’m not familiar with the matter.

Google Translate has major gaffes in many of its less common languages. This is nothing particular about Assamese.