In my country, I am taxed on capital gains.
Say, I make BTC online and I did not buy any bitcoins. Would I have to pay capital gain tax or add the income I make to the yearly tax return, I have to submit? Because this is a additional income, and not my primary income, derived from my normal work.
I do not want to use an exchange, to convert my BTC to cash, because it asks for too much personal information.
What other methods are there, to still pay tax, but not to use an exchange?
There are no capital gains until you sell those coins. Even then your country's tax rules may not require you to pay capital gains taxes, depending on where you live, how much it was, or how long you held them.
In addition, and depending on your country, you may have received income by receiving those coins. It would be classed as a barter exchange. Look into your tax laws.