How to manage customer contacts

preuley30 Happy Workday to you.

Respectfully, I don't think creating a distribution list will resolve your issue unless you share it with others. I found Microsoft's Contact Sharing documentation, an alternative method for you and your team. This method, too, has its pros and cons.  

You can share your contacts with specific users using only MS Office Outlook. However, Outlook for the web does not support this feature.  

Resource: https://docs.microsoft.com/en-us/outlook/troubleshoot/calendaring/how-to-share-calendar-and-contacts#which-email-client-is-in-use-if-you-want-to-share-contact

I also found an article titled, Convert a user mailbox to a shared mailbox. I was hopeful. This option has its advantages and disadvantages as well. So, therefore, I don't recommend it for a small business. There were too many variables that may be problematic long term. Here is the article anyway. 

 https://docs.microsoft.com/en-us/microsoft-365/admin/email/convert-user-mailbox-to-shared-mailbox?view=o365-worldwide

I searched for "simple" Outlook Contacts Sharing Add-ons. I came across Pobuca in Office 365 AppStore. After investigating the product reviews, I don't recommend this product. I struck out again. 

https://www.capterra.com/p/148335/Pobuca-Connect/reviews/

In summary, I didn't provide you with the best solution. At least, you know which product Not to Use. Sorry, I wish I was more helpful.