any online solution consists of you paying money through some sort of payment processor, whether you use credit card, paypal, webmoney,.... they all have some sort of information (ID) about you.

if you want no one to know you bought bitcoin then you have to buy it with cash, face to face

if you want no one to know what you did with the bitcoin you bought, you can buy with conventional ways and then use other methods to cover your track (search for detail). like mixers to mix your coins and using an altcoin toe exchange to altcoin and back to bitcoin again.