I'm sorry you're upset for missing important emails: it's unfortunate and I apologize for any confusion that was caused by DreamHost. I brought up this conversation to the domains product managers and they're going to work on your suggestion below. Let's try to be constructive and improve the process.
For future readers, let's be clear: there is no email from name-services.com! The only emails you should have received and read are from dreamhost.com and dreamhostregistry.com. Name-services.com is a URL linked from the email sent from dreamhostregistry.com.
It's unfortunate that you rely only on whitelisting or any spam filter to be 100% reliable: it's unsafe practice... I suggest you to review your policy for the future.
There is no such email, not from name-services.com. If you have received one, please share it with the full headers.
Ok, let's focus on this part: DreamHost does communicate to customers that they should expect an email from dreamhostregistry.com (there is no email from name-services.com. I've already highlighted to you the documentation that mentions how the domain verification works: https://help.dreamhost.com/hc/en-us/articles/217083957-Domain-verification-policy .
I had colleagues dig into your account: this is an excerpt of the content of the email you have received from DreamHost on July 14th, concerning you buying a new domain name. The message from DreamHost says at one point:
Verify Your Contact Info
If you haven't verified your contact info before, you will receive an e-mail from firstname.lastname@example.org asking you to verify your name and e-mail address.
And here is the first email that you missed, this one comes from dreamhost.com. The other email you missed comes from email@example.com and this email contains a link to name-services.com. Apparently you missed this one too.
From what I understand, such emails from DreamHost were caught by your aggressive spam filters.
This is a good suggestion: show a more prominent notification of the domain registration process on the web pages, when the sales is completed.
I want to apologize again for the miscommunication: DreamHost can always improve its processes. I hope this incident also serves as a chance for you to review your policies for checking email spam folders.