Service has to be done in a proper name and followed by using the procedure given in sec 282 . How ever in your case , 292B can be invoked , cos it looks like an error . It will be deemed service . Just by not having or having Pvt in the name is not a sufficient cause to challenge the notice . If it served properly at a proper address , with the proper name ( with or without Pvt ) , i think its deemed service .Looks like an error , 292B likely to be invoked .
Is it a notice u/s143(2) ? If pan number is not there on the notice , they wont be able to take the print of the notice .
I am surprised , is it a handwritten notice ?Notice is served under what section ?