How do I choose a package name for a custom Perl module that does not collide with builtin or CPAN packages names?

The namespace Local:: has been reserved for just this purpose. No module that starts with that prefix will be accepted to CPAN or the core. Alternatively, you can use an underscore in the top-level name (like My_Corp::Session or just My_Session). All categories with an underscore have also been reserved. (This is mentioned in perlmodlib, under "Select a name for the module".)

Note that both those reservations apply only to the top-level name. For example, there are CPAN modules named Time::Local and Text::CSV_XS. But Local::Time and Text_CSV::XS are reserved names and would not be accepted on CPAN.

Naming modules after your company is fine too. (Well, unless you work for some really generic sounding company.) Using the reverse domain name is probably overkill, unless you intend to distribute your modules to others. (But in that case, you should probably register a normal module name.)

How Perl resolves a conflict:

Perl searches the directories in @INC for a module with the specified name. The first module found is the one used. So the order of directories in @INC determines which module would be used (if you have modules with the same name installed in different locations).

perl -V will report the contents of @INC (the highest-priority directories are listed first). But there are lots of ways to manipulate @INC at runtime, too.

BTW, Raku can handle multiple modules with the same name by different authors, and even use more than one in a single program. That's a different solution.

There is nothing wrong with naming your internal modules after your company; I always do this. 90% of my code ends up on CPAN, so it has "normal" names, but the internal stuff is always starts with ClientName::.

I'm sure everyone else does this too.

What's wrong with just picking a name for your package that you like and then googling "perl the-name-you-picked"?