Can I have my own health insurance while also being listed as a dependent on my parents?

I’m 21, male, and a student at a large university in the US. I also do not have a good understanding of how this all works. My university is able to provide students with health insurance.

I want to be on my own health insurance because my parents essentially do not believe in modern medicine.

I have not been to a primary care physician in at least a decade, the only doctor they have taken me to in that time is a holistic one.

I am mostly unvaccinated because my parents have strongly held anti-vax beliefs that I do not share. I don’t make much money though and do not want to pay to get vaccinated entirely out of pocket. Nor do I want to use their insurance and risk them finding out.

I have a couple of medical conditions, such as some severe stomach irritability that often leads to acid reflux and nausea, and ulnar impaction syndrome. The former my parents only have ever taken me to a holistic doctor for, and while they never helped the issue partially resolved itself so I stopped wasting my time trying to get them to help me with it. The latter I finally saw a surgeon for after dealing with some excruciating wrist pain for over a year and a half, and even then only because the holistic doctor told them they need to take me to see a surgeon. I ended up getting steroid shots for my wrists, which will help temporarily, and likely will need surgery eventually on them, but I plan on waiting until I have my own income and health insurance for that to avoid discussing it with my parents anymore. I would like to see a doctor about my stomach issues with the concern they could be related to an ulcer, but my parents have refused to take me to one enough times that I’ve given up asking.

For various reasons I’m fairly certain I have ADHD, something a doctor actually mentioned to my parents when I was around 8 years old and still seeing a regular doctor alongside the holistic one. However they essentially believe the condition isn’t real, and from my understanding, the doctor saying this to them is part of the reason they stopped taking me and my siblings to regular doctors altogether. Regardless, it’s not as important as the other reasons I listed but I would like to speak to a doctor about this.

Despite all of this, I do want to stay as a dependent on their health insurance for a couple of reasons.

My dad is very successful financially and his company provides us with very good health insurance. If anything severe were to ever happen to me, from my understanding it would be in my best interest to be on his insurance. This is the main reason I want to stay on his insurance as long as possible.

I don’t actually want them to know that I am no longer a dependant on their insurance because they would question why I left it.

Apologies for the long post, but in summary, my question is whether I can simultaneously acquire my own health insurance through my university to use for the above-mentioned reasons, while still being listed as a dependant on my dads insurance.