Hi, @CFTEA! So you've got a giant list of just names and email addresses. You're not alone! Let me see if I can act as Virgil and guide you through at least a couple of those circles...
I think when you see stats like "10x a day," they immediately make you feel like you're doing something wrong. If you were to send 10 emails to one person in a day, they'd most likely mark you as spam and block you! Organizations that do that may be sending lots of emails, but they've probably targeted each email to a different audiences (using segmentation), so the same contacts are not receiving all 10 emails.
Segmentation can also help with the contacts that think you're sending too often. They may not be seeing value in the content you're sending. This could be too much info packed into one email where the important parts (to them) get lost. Segmentation helps you group contacts by their interest, letting you shorten your emails. You end up sending more emails overall, but they're shorter and targeted for a specific audience. For the nuts and bolts of how segmentation works, check out this article.
Ok, that being said, how do you do it? There are an infinite number of ways to segment, so hopefully this will help you get started and make some changes to better segment your contacts moving forward. Let's start with your current contacts...
If you're only working with names and email addresses, you can segment them by their opens and clicks behavior, or by their engagement level. Your contacts provide all this info themselves just by opening and interacting with your emails, and you just have to "ask" for these contacts by creating a segment. This article can get you started.
Next, start using click segmentation in your existing email format. It lets you add contacts to a list based on the links they click in your email. It's an easy way to gauge interest. (This article explains it all.) Then you can create a segment and send only to the contacts on that specific list.
Another quick thing you can do is to make sure the "Update Profile" link in your email footer is enabled and customized - if your contacts click on it (and you can absolutely get creative and draw attention to it in the body of your email), they can tell you which lists they want to be a part of and enter in missing contact details. This article can show you how.
And finally, there is also a way to "bulk update" contacts using a spreadsheet - there is a little data entry involved but it can be done over time. It works like this: You export all of your contacts into a spreadsheet. You create new columns based on the contact information that you have and start filling it in. When you're ready, you import the spreadsheet back into your account as if you're adding new contacts. It will update existing contacts with additional contact details and custom fields as long as the email addresses match. Then you can start segmenting by those things. For instance, you can create custom fields for the branch and send a message only to a specific branch.
Now let's tackle new contacts. A great place to start segmenting is with your sign-up form. All of our sign-up forms let you choose which contact details you want to collect so that going forward you're building segmentable info into your contact records from the start. If I haven't bogged you down, read this article for more details.
It's a lot of information, but take it one step at a time. Good luck with the new branding! Let us know how it goes!
The segment of reaching back out to those that had been missing was very helpful, but I can see we can do so much more. Thank again for your time and the great details that I can continue to research! 
