Ownership of a flat

The flat should be vacant, it should be occupied immediately after giving advance through agreement, and finally registration should be done.  Speak to your banker for further guidance.

Supposing I've no dues with the bank or the real estate company but the registration is pending. In that case, is the property in my name (in the documents)? 

Please use the Forum only for taking guidance and not for quz.

One must have a valid title deed in his name with due legally valid registration and should be in possession of the property for claiming ownership of any property.

Claiming ownership is different with bonafide legally valid ownership.

Registration may be kept only for prescribed time frame as per their norms.  If the execution parties fail to compile the formalities, documents are not documents till they are properly registered after compiling the formalities.

For Bank loans, there is no effect on title, and the property is only a security for Bank loan.