It's just a matter of the name. The name Rajdhani is used for the train connecting the State capital and New Delhi. AP AC SF should be enough for you. Also, as of now, there won't be much patronage for a fully A/C express running with few stops. Better to have the AP AC SF with good number of halts in the state and limited halts outside the state. Besides, more important thing for the state now, is good intra-state connectivity. As of now SJ, link and this AC SF ( after schedule is speeded-up) should be able to satisfy the demands to Delhi, One train to Delhi from TPTY ia NLR-OGL can be considered to round it off.