If you buy a car or a bike on loan paying emi then RC would contain the name of financier or bank which offered you loan. This is to ensure that you can’t sell the vehicle as it is part owned by them unless you pay your loan and get it removed. 
Once your loan is paid or closed by bank or vehicle financier you need a NOC from them mentioning loan has been paid or closed , then you need to visit nearby transport authority from where the RC was issued to ask them for fresh RC without the loan finance cos name.
Here is the detailed procedure to Remove HYPOTHECATION from RC of any two wheeler/four wheeler vehicle in Delhi.
- Form 35 duly filled (for deletion of Hypothecation)
- NOC from financier on letter head.
- Registration Certificate (original).
- Self attested photocopy of valid Pollution check certificate.
- Self attested photocopy of valid insurance certificate.
- Self attested photocopy of one govt issued photo id.
- Self attested photocopy of one govt issued address proof.
- Fees of Rs.300-1000 in cash depending on vehicle & for new RC card.
Issuing Authority is mentioned in current RC only. You need to visit same transport authority to get this new RC without the name of loan provider. First you need to visit & submit the docs, after 5-15days they would either call you for new RC or would speedpost you.
After getting this new RC you would be complete owner of the your vehicle & can resell it further without any issues.