How do I save the domain names I have chosen from the lists?

You can register domain names on our lists with the registrar of your choice.

We recommend those whose main business is this, such as Netim, Namebay, Nameshield, InternetBS, SafeBrands, etc. Surprisingly, the best-known registrars are, in our opinion, often the least efficient, like Godaddy, OVH or Ionos/1and1

To go further on registrars

https://www.refdomaine.com/annuaire/registrar/index.html : Review of all the main registrars on the market