Should I just provide fake info into registration form?
Certainly not. If you read all fine prints in the contract between you and the registrar you will choose to buy the domain, contract that will reference also the contract between the registrar and the registry, you will always see clauses akin to:
"Providing false information is ground for domain name ...
As Patrick Mevzek said in his comment, it's because registrars can have resellers.
This is the response I got from CIRA.
Name.com is a reseller for other Registrars, and in this case they are for at least one certified .CA Registrar.
Certification is a process that requires some strenuous testing on the Registrars side. They also have to agree and ...
Host a DNS server at home, set it up so the domain points to your static IP. Maybe use https://www.virtualmin.com/ for this, makes life much easier.
Register a .com domain (this will cost you $, see for example https://tld-list.com/tld/com) and tell them to set your DNS for it.
Pay for power which your server consumes ;)