I hate to be so cynical if it helps people, but with his name plastered in the company and site like this, it feels like prep for a presidential run or some other political office.
If I'm understanding their basic message, the pitch is "we can get you cheaper prescriptions because we're a well run business that's making a rational but not exorbitant profit" and linking your branding to someone already famous for running businesses seems to be a very reasonable way to add credibility to that message.
In other words, I don't think Cuban puts his name on all businesses he's involved in like this, but for this case specifically it seems fairly obvious that using his name furthers their message.
I assumed it was to help add legitimacy to the company. Some random company selling drugs for cheap on the internet? Sounds very sketchy, stick with your local pharmacy. That same company, run by a famous figure? Maybe worth giving a shot
Or Disney or Ford or McDonald's or Goldman Sachs or 1000s of others. Even in pharmacy, Johnson & Johnson, Pfizer and many others are named after founders.
In other words, I don't think Cuban puts his name on all businesses he's involved in like this, but for this case specifically it seems fairly obvious that using his name furthers their message.