Author names are displayed on the library view in the same way they are entered. If you enter Firstname Lastname, that is what you see. If you enter Lastname, Firstname, then that is what you see.
With some work you can convert from one form of author name to the other. See this section of calibre's FAQ
, and in particular the boxed note at the bottom of the section that discusses changing from FN LN to LN, FN. There are also a zillion posts on this. Search for "author sort tweak" to get some of them
Note that you can change which author name is displayed in the tag browser using the tweak "Use author sort in Tag Browser" (categories_use_field_for_author_name). Change tweaks using preferences -> Advanced -> Tweaks.