Khb allotted site can be registered along with parents

You are a separate/ private individual for all purposes including registration, allotment or purchase of property from anyone.

If the housing vacant site has been allotted to you by KHB, then you may have to pay the requisite fees and comply with neceessry formalities in order to enable the authorities to execute a registered sale deed in your favor after which you can independently enjoy the property purchased by you,.

If you have added their names in the sale deed, your parents will have equal rights over the site along with you.  You will have a right over the site only 1/3rd share. And the KHB will also agree to add your parent names. So you can decide.

You may not be permitted to add your parents name in the registered sale deed if you are the sole applicant.

After purchasing it and after complying with the conditions of allotment, if law permits then you can transfer a portion of property to your parents to make them as joint owners along with you.

The plot / site is stated to have been allotted in your name, accordingly you are sole titleholder.

If you want to add name(s) of your parents in the property, you will have to execute a gift / sale deed etc.