replacing user name with full name under "published by" on articles

Do not edit the Twenty Eleven theme. First create a child theme for your changes.

Got it.

Now what do i modify?

Thanks! ??

the code is using https://codex.www.ads-software.com/Function_Reference/get_the_author

which ‘Grabs the value in the user’s Display name publicly as field.’

do you want to show ‘first name’ and ‘last name’?

even considering that these are not required to be filled-in for users?

you will need to edit functions.php in the child theme;

add either edit a copy of the function twentyeleven_posted_on() and change this line esc_attr( sprintf( __( 'View all posts by %s', 'twentyeleven' ), get_the_author() ) ), to replace get_the_author() with some code to retrieve the full names;

relevant WordPress function:
https://codex.www.ads-software.com/Function_Reference/the_author_meta

or add a filter function for ‘the_author’; https://codex.www.ads-software.com/Plugin_API#Filters to do the same.