Can I go to the bank and get money when I don't know my account number, don't have a card by just giving the my name on the accounts?
Your money in the bank is yours. If you lose your bank card and forget the account number, it's still yours. It's just harder to prove. If your name is Joe Smith, it might be harder to find your bank account and to prove it's yours.
If "go to the bank" means walking into a branch of the bank and walking out with your money fifteen minutes later, that's unlikely to happen. More likely they will give you forms to fill in to maximise chances of finding your account, and tell you what evidence to bring to prove that you are the owner of the account.
I have seen the notation KTB written on documents in the place where you put an identifying number of some kind. It stands for Known to Branch and means the tellers recognize you. It's been written on documents of mine when I was depositing cheques large enough that someone else had to come and initial the transaction, and I presume that some people might have also had to show extra ID, but I didn't.
Just a month or so ago I was in line behind an old man at a branch where everyone has to put their card in and enter a pin to do transactions. I heard him tell the teller "I don't have a card. Never did. Don't hold with that." Another teller came by and said something quietly to the teller (I presume it was "that's old Mr Smith, we all know him") and the transaction appears to have taken place without any ID being passed across the counter.
So yes, at least in Canada, if the tellers recognize you, the requirements for ID are less than you might think. It's a bit of a long con to spend 25 years going into a branch and conducting all your business under a particular name, just so you can do a transaction or two without ID, though :-)
In Finland, this happens all the time - it's all about having an official ID, they don't even ask your bank account number or the card.
However, as no location was specified in the question, I guess it could be anything. The stronger the requirement for official personal id is in your country, the better odds you have with just using that. Where I live it is quite strong.