If you own your company name do you have to buy the domain with your name? Will you still own it? [I Design Websites]

I have many questions and helping a friend build one. I've looked online for some answers, but I have more questions.

Where do you go to register your domain name.

If you use a website builder like wix, etc. Will they own the name?

Do you have to pay for a name you already own once it becomes a domain name?