These days most trade names like this are made up by marketing departments precisely because the company believes that they have NO "meaning" and so the public will be able to identify the word only with the product.
The
Eli Lilly company may be reluctant to give out information about exactly how they came up with this name precisely because it turned out to also be a human name. Cialis is a surname found in England,
France,
Ireland, and Canada, at least, and if you Google "
Russell Cialis" you will find many references to that particular man, a public relations consultant in England who threatened to sue the company when they refused to change the name because of possible embarrassment to his family.
I would bet that the Hispanic girls named Cialis have NOT been given the surname Cialis as a name, but that their parents independently invented it, as -lis has been one of the most productive suffixes in Latin
America among parents who create brand new names for daughters over the past several decades.