Thanks for asking about this. We are working to make this a bit better so that your contacts are there via a variety of means, though it's not always that obvious.
From the contacts tab in the web browser (though it's better in the downloadable client), you can bring in your Google or even Exchange contacts into the DIGITS experience. Right now, the contacts aren't yet persistent - we are working to federate the IDs so that you can always have access to your Google or Exchange contacts - that will come soon.
The second way to have your contacts available is to use the DIGITS application on your phone (even if you use it briefly). From there, you can upload your contacts and those contacts will be available when you log into the web browser as well.
Both of these methods work and we are working to improve this experience and the customer education to let you know how to get your contacts in to the DIGITS ecosystem.
Thanks for reaching out.
It's about a year later since this last post and you still can't add a name to the phone number on Digits. Verizon messenger very simply allows you to left click on the number, add the persons name, save it and done. What are your plans to solve this simple problem?