thank you very much!

Is there any Bitcoin services that are known to keep anonymity? A bitcoin arena that
It's known not sharing the information with 3th parties or governments?

I want to ask about anonymity when I pay with Bitcoin. My question is whether when:

1. I register for an online trading arena that does not require personal identification
2. And I buy Bitcoin with my credit card
3. I pay someone with Bitcoin:

I know that my wallet address will be expose on the blockchain, but since I did not identify myself,
 my question is, can anyone (the person who received the money, government, etc.)
 can get to my identity just because I bought the bitcoin with my own credit card?

I would love to hear any opinion as well as recommendations on how to make transfers in complete anonymity. Thank you! <3