Cardano was named after the 16th century Italian scientist Gerolamo Cardano; given the people designing the platform it makes sense to name it after a scientist, but is there any reason to specifically choose Cardano? I only know him for publishing general solutions for cubic and quartic equations. I did a quick search on the foundation's website and forum but found nothing about this.
I think the answer you are looking for can be found at the 3:10 mark (bold part in the transcript below) on this video, but for the consistency of ideas please watch from the 1:43.
The transcript of this portion of the video is:
Gerolamo Cardano (1501–1576) was an Italian mathematician, physicist, biologist, physician, chemist, astrologist, philosopher, writer, and gambler. During his lifetime he wrote over 200 scientific works and was one of the key figures in the mathematical field of probability during the Renaissance. Gerolamo Cardano, is well known for his achievements in algebra. He was a teacher in Milan Italy in the 16th century. In his 1545 book Ars Magna, he made the first systematic use of negative numbers in Europe, published with attribution the solutions of other mathematicians for the cubic and quartic equations. He also acknowledged the existence of imaginary numbers now used in geometry. His book about games of chance, Liber de ludo aleae written around 1564, but not published until 1663, contains the first systematic treatment of probability. He used the game of throwing dice to understand the basic concepts of probability. He demonstrated the efficacy of defining odds as the ratio of favorable to unfavorable outcomes. For a cryptocurrency project that is looking to utilize scientific methods based on mathematical proofs and game theory to build highly flexible and interoperable money, I think this choice seems to match perfectly.
"I only know him for publishing general solutions for cubic and quartic equations."
In 1550 he also introduced a cryptographic writing tool called the Cardan grille which uses a grid.
The answer by Dacomis points to a video by a Youtuber named "Crypto Jerome" where Jerome says that "Cardano the project is all about innovation" and "Cardano the man was all about challenging the status quo", which is what he says immediate after the transcript given by Dacomis. While this could be what Charles Hoskinson had in mind when he chose to name the platform after Cardano, there's also other people throughout history that used the scientific method and mathematical proofs, so it could just be that Hoskinson was a fan of Cardano (like I am).
Another relevant article on this topic is "Cardano – Inspired by Legends of Science & Math" which talks about how the platform was inspired by legends Gerolamo Cardano and Ada Lovelace, but again the article's content is not coming directly from Charles Hoskinson.
To really find out the answer to this question, you'd have to ask Charles Hoskinson (or find a source that got the answer from him, such as an interview).