I have a date field (field_date) and on the right of this field I have to display the day of the week
You can change how dates from date fields are displayed by changing it on the
Manage display (/admin/structure/types/manage/[my_CT]/display) page for that Content type.
Custom date format for individual field
The quick and dirty way of doing it is by choosing
Custom for Formatter and entering the code for the date, for example:
will give you "2019-09-09T17:30:19, Monday".
You can lookup the various date and time codes in the PHP manual: https://www.php.net/manual/en/function.date.php
Overriding individual fields displays with custom date formats isn't the best way to go because you can't reuse it throughout the site, for other fields, or translate into other languages (different countries have different conventions about how to write dates).
Reusable Custom date format
The best way is to first add the new Date format to your site. This way you will be able to use anywhere where you can format Date output.
Configuration > Regional and language > Date and time formats and Add a new format.
Name it so it makes sense to your case, enter the PHP date code you want into the
Format string, select Language and add the format.
Now visit your Content type's
Manage display page and change the
Formatter of the Date field you want to affect to
Default, and the
Date format to the one you have just created.
If your question is for showing the day on the content create/edit form, and not displaying after saving that form (which I answered in the previous answer), you'll have to change the widget for the date field.
You can do that through some custom code, but I believe the Bootstrap Datepicker module can do that too (I haven't tried it).
That module has the
Date format option where you can enter for example
in the Date input field after selecting a date from the calendar popup.