If my PAN card only contains only my first name but my plane ticket contains my full name, will I be allowed to board a domestic flight in India?
The Airport Authority of India has deployed CISF (Central Industrial Security Force) to carry out the airport security functions at 52 AAI airports / civil enclaves while at remaining operational airports /civil enclaves, the State Police carries these functions. Its important to note that the discretion to allow a passenger/s inside the airport premises lies solely with the concerned CISF official/state of security at that airport. If the concerned official is satisfied with the valid i.d. proof, only then he/she will grant permission to enter the airport.
Similarly, you will have to satisfy the question mark look of the airline staff if they do a thorough id check.
Since the PAN only mentions the first name and little else, it would not be wise to rely only on that document as the sole means of identification. Even if you were to be allowed inside with some fuss, chance are you will have that much lesser time to complete the boarding formalities. If possible, do carry additional government issued photo identification with the full name (Driving License / Aadhar / Passport) to be on the safe side.
As per my personal experience when I traveled from New Delhi to Bangalore in 2009 for some MBA Interview and GD via Indian Airlines. There they asked me for any Photo ID proof with the E-ticket I have, I presented them my Driving License (as I didn't have PAN Card at that time). And I think, now-a-days security system has got better than old times.
But my Driving License was too old (blurry because of lamination and keeping the same in wallet for long time) to read, so they asked me for a different proof as the staff member told me 'This is not acceptable, your name and photo is not clearly visible' (something like this). Luckily I have my passport with me (because that was my very first flight and I thought even for domestic flights passport is required so I kept it with me).
It is always good to carry a second ID proof as a precautionary purpose or for Plan B, since then I always carry multiple ID proofs (just to avoid the future hassle and waste of time & mind).
Also, this link states that you should have at least one Govt. issue Photo ID proof with same name as on your ticket.