So you already have one WordPress website hosted with SiteGround, and now you want to add another one to the same hosting account but with a different domain? That's easily achievable, as long as your SiteGround plan is 'GrowBig' or above (ie not the entry-level 'StartUp' plan).
1. Register/purchase your second domain. I use 123 Reg for this, as I like to separate domain registration and hosting
2. Log into your SiteGround account, click on My Accounts, and Go to cPanel
3. Add the new domain using the 'Addon Domains' tool in the 'DOMAINS' section - Siteground have a short guide to doing this so I won't repeat the steps here. But as I mentioned, this tool is only available to customers on the 'GrowBig' plan or above
4. In SiteGround > My Accounts > Information & Settings, make a note of your nameserver details. There should be a pair of nameservers, and the details will look something like this:
(You can also see your nameserver details in cPanel, in the 'Account Information' section in the top left)
5. Back in 123 Reg, Manage your new domain and then Change Nameservers (DNS)
6. Enter the Siteground nameservers in the 'Nameserver 1' and 'Nameserver 2' fields, then click Update
7. You now have to wait for the change to propagate. 123 Reg says this can take up to 48 hours, but in my case it took around 12. Once this has happened, if you view your domain in a web browser it will no longer show this 123 Reg holding image:
And will instead show something like this 403 Forbidden error:
8. Now go back to Siteground, My Accounts > Go to cPanel > Softaculous (in the Autoinstallers section)
9. Hover over the WordPress icon and click Install
10. Fill in the details, taking care to select your new domain in the Choose Installation URL section. Click Install
11. The installation process will take a minute or two, after which you should be able to visit your new domain and see the default WordPress theme (currently Twenty Nineteen)!