You are covered as a beneficiary under your father's health care coverage provided by the company he worked for until age 26. Just as with a life insurance policy any dependent listed as a beneficiary at the time of death receive the said benefit, in this case healthcare coverage under the Affordable Care Act which covers you up until the age of 26 at which time you will have to get your own policy or have one provided by an employer.
You are listed as the policy holder now because you are the benefactor and the policy must be in the name of a living person. Even though your father was the original policy holder, since he is no longer alive he cannot be a policy holder that is required by law.
If your father's company employees more than 20 people you can also be eligible for even further coverage beyond your 26th birthday. COBRA also known as the Consolidated Omnibus Budget Reconciliation Act enables you to buy and extended healthcare coverage of up to thirty six months. If you elect to do this you need to contact your father's former employer in writing within sixty days of your 26th birthday. Some states allow this for employers with less than 20 employee, you will need to check your state's laws if that is the case.
Another rule in the benefit that many people do not realize is even if you get married between now and your 26th birthday you will still remain covered by your father's policy until your 26th birthday regardless of your spouses health insurance policy. Some people do find their spouses policy has better coverage, lower deductables, etc.. That is something you and your spouse would have to analyze and determine if that situation arises for you.