I'm a music arranger, and I am preparing a series of string quartet pieces. I want to use an "Inspired by the Netflix series 'Bridgerton'" phrase (or some such phrasing) on the packaging and search strings. Is this legal?
What you need to ask yourself is: Could they sue you, and what would it cost me? Would they want to sue me? Would they win? And what would that cost me?
If they sue you, even if they don't win, it can cost you a lot more money than you can afford. This is not a risk that I would take.
(Whether they would win depends on how you present their name, and whether they can convince a judge that you use their name to make people wrongly think that you are connected to the film series).