I don't have my last name in any of my documents what can i do?

If you wish to add a second name then right procedure is getting a notice published in a local News Paper, regarding your intention to change your name/or add surname to it, and subsequently get it published in Gazette of India. These days Gazette prints have been discontinued, so you may have to check with concerned press in your city, if they still print the Gazette Notification, or it is given to you in soft copy. Once Second name added then applications can be made with the changed name certificate to all the concerned departments to issue a fresh certificate with changed name. 
To get a birth certificate you have to go to Municipality and contact Birth Registration Department of Municipality. Only they can give you a proper Valid Birth Certificate.