"All of the texts I looked at started with a package and a sub called 'new' to create the object."
It is convention to name constructors new but there's no requirement to do so. You could just as well call it old or frangipane and it would make not one whit of difference to the Perl interpreter. But the reason that you should call a constructor new (and not old or frangipane) is for humans reading your code. When they see new they'll know precisely what that method call is doing!
That said, it's quite common for a class to define additional constructors such as new_from_json or new_from_yaml in addition to their standard new constructor. These are often wrappers around new that do additional pre-processing or post-processing.
package Cow { use Moo; has name => (is => 'lazy', default => sub { 'Mooington' }) } say Cow->new->name
