Silly question: where do I add customers and their contacts to SWSD?

You can track Vendors in the Procurement section. You may be able to use this to track customers as well. You can also add Contracts from the same area, which have some additional fields for contact info. 

I'm not sure this is exactly what you're looking for, but it might work for you.

Alternatively, you might need to use the CMDB, which allows you to define custom items like "Person" that can then be created and tracked in the Service Desk CMDB section.

I recommend going with the CMDB option. This will give you more flexibility to add custom fields that you need for your customer records and allow you to easily connect them to other CIs in the system. Here is the documentation around the CMDB and how you can create custom objects for it documentation.solarwinds.com/.../cmdb-admin.htm

Thanks, Joey. After lots more looking, this is the way to keep their info together and link them to their assets.