When you buy hosting from WP Engine the WordPress installation process is a little different to that on many other shared hosting platforms.
The moment you sign up for your account, a WordPress installation will be set up for you. That is true whether you get a Personal account which allows only one WordPress site to be installed, or a Pro account which allows up to 10 to be installed.
Your Site Starts Life As A Subdomain Of WPEngine.Com
Each WP Engine WordPress installation starts life as a sub-domain on WP Engine. So when I initially decided to run Genesis Clubbers on WP Engine, it started out as myaccountname.wpengine.com. Later when I was ready, I pointed my domain name at the WordPress installation and the site became accessible via the proper domain name.
WP Engine Installation Names Are Unique
You can delete an installation at any time – but – be aware that you cannot re-create the installation using the same install name. So if you first WordPress installation is called mysite, then if you delete it, you will not be able to use that name again.
Also be aware that the install names have to be unique across the entire WP Engine network.
The only way you can reuse the name is to contact WP Engine support and ask them to reset the installation back to the default.
In a sense, the install name you choose does not really matter as, assuming you set things up properly, no-one will see it apart from you. However it is nice, especially on the Pro account where you can have up to 10 installs, to have a naming convention.
Use An Install Naming Convention
For mine for example I create a two letter install shortname, and then prefix that with a word consistent with my brand. So for example I might call each of my installs diywebmasterygc, dimwebmasterygb, diywebmasteryvp for genesisclubbers.com. genesisbluprints.com and veganpoetry.com, respectively.
That way, when I look at my list of installs I can easily see which underpins each website.