Yes, you can claim your own invite link by signing up in the Feeting app. Go to profile and claim there your unique and memorizable invite link. For instance https://feetwith.me/johndoe.
This link is now officially yours and cannot be claimed by anybody else. You can use it in all your Feeting invites as of now. The sooner you claim your link, the likelier you can claim your first name or first name and last name. The link will be yours forever until you change it. Go for it.