Now I can’t log into my account. I didn’t reach the legal age before, so I couldn’t pass the game verification, so I randomly found an adult identity verification. But now I am an adult and want to change my account. I cannot contact your customer service due to jet lag, please help me.
Jet lag means you are very tired from traveling. To contact customer support to do a full name change on an account you put in a ticket through the website with the proper legal documentation.
Blizzard does not allow account transfers except between a parent and a now adult child. That requires the legal paperwork to prove. If you selected a random adult name then you are not likely going to be able to get the name changed to yours. Further, it is technically against the rules for you to even play on an account not in your name. (minor child is the exception).
Account Name Change article Blizzard Support - Updating the Battle.net Account Holder Name
The ticket link for the support request is in the article. You will likely need to provide Govt Issued ID both from the first person who is the account holder, and yourself, along with proof of legal guardianship relationship (parent/child).
Providing Govt Issued ID (what is accepted and how to cover things then submit it). Blizzard Support - Providing Supporting Documentation