Hi @jfuellgraf, thanks for your interest in Let's Encrypt.
I would like to suggest looking over
which is a discussion involving at least two other companies with potentially similar problems. (I have also had an e-mail exchange with some other folks about best practices in this area which I can dig up to try to see what recommendations I can offer, and I think there may be an additional thread on this forum that also relates to this topic.)
I didn't understand whether you want all of the certificates to have the same name, or whether you want them to have different names.
There is no licensing required for use in commercial products in general, but there are likely significant limitations related to the rate limits
because these would not by default permit obtaining thousands of certificates under the same domain name. If your customers somehow have or could acquire their own domain names instead of your company name, you would be in a much simpler position with regard to the rate limits.
I'm quite happy to discuss this further, but I suggest you read some prior forum posts from the thread I mentioned and see if they help answer any of your questions or suggest other questions.