It wasn't immediately obvious to me that license features could be used to implement user registration, but Wyatt set me straight via email. I just wanted to post this here for the community's benefit. Here's the email exchange:
geekherder:"We sell licenses via a reseller channel as well as to large institutions where the purchaser may not be the actual software user. It seems that our support organization would be better able to help our customers with licensing issues if they could look them up by name, company name, etc."
Wyatt:"LimeLM does allow you to set other fields for a license. We call them "license features" (see: http://wyday.com/limelm/help/license-features/ ). So, for instance, if you wanted to have "Purchaser Name", "Company Name", and "Company VAT", then you can create a license feature for each of those.
Then when you create a product key those fields will be visible and you can set them. You can also set them via the LimeLM web API, so this can all be automated for resellers.
You can have as many "license features" as you want. And they're visible and searchable"