Whose name should the domain and hosting be in?
The domain should always be in your name. Someone else can manage the hosting, but you should hold the access details too. That is how you keep your site when you change partners.
One of the most frustrating problems a company can have with its website isn't technical at all: the person who built the site years ago can't be reached, and it turns out the domain is registered in their account, in their name. If the domain isn't renewed, both your website and your company email stop working.
Domain, hosting, site: three different things
Domain: yourcompany.com. It is bought yearly from a registrar. It is the address of your website and your company email.
Hosting: The server where the site's files live. The domain takes visitors to this server.
Site: The files, the database and the content on the server.
All three can be with different companies. What matters is knowing who controls each one.
Why the domain should be in your name
The owner of a domain is the person or organisation listed as the “registrant”. Your company's name should be in that field, and the email address on the management account should belong to your company. Your agency can manage the domain for you, but you should be the owner. That way, when you change partners, you can move the domain elsewhere with no trouble.
Where the hosting can be
You can keep the hosting in an account opened in your name or on the server of the company that runs your site. The second is usually less hassle: updates, backups and security are handled in one place. What matters is agreeing from the start that, if you stop working together, you can take over your site's files and database in full.
What you should have on hand
The login for the domain management account and the domain's expiry date.
Where the site is hosted and who manages the server.
A login to the site's content management panel.
The management details for your company email accounts.
Where the latest backup is kept.
Keep these details somewhere safe, such as a password manager, where more than one authorised person can reach them. Put the domain's expiry date in your calendar and turn on automatic renewal.
Ask when you get a quote
The answers to “Whose name will the domain be registered in?” and “If we part ways, how do we take over the site?” should be agreed from the start. At Methodda, for clients who want it, we set everything up from the domain to the server and keep the site running; for those with their own server, we deliver the site there.