The second piece to this is how the GUI works. Instead of showing long bit strings or hex encoding them in some pointless way, it allows you to assign names to these addresses as you come across them. When you see the address in some other page it will show up with the name you assigned and so you will recognize it.
A key point to this is that HTTPS does not actually cause you to know you are using the right domain name. Aside from the fact that HTTPS is untrustworthy due to the CA model, mybrand.com or mybrand.net or one of the other infinite number of legitimate sounding things could all be the correct domain for some brand, you would never know unless someone previously introduced you to the right domain name. Since you had to get it from somewhere, you may as well have received the public key at that point, which could be encoded in a QR code, or, on the internet, which is the main use case of petnames, trivially included as a link in some web 8.0[1] page or chat where you first heard of the brand.
1. I guess it will take them 6 more tries to get this right.