Dear Balu,
i have recently got the German citizenship and had the same problem created by some ignorant clerk in indian passport office in india around 20 years back for which i have suffered around last 15 years .....my fathers full name was added to to my firstname even though Indian passport have a separate field for father's name on the back , anyway.
after i got my Einbürgerungsurkunde i went directly to Standesamt to apply for change of name under
Art. 47 EGBGB , so that i can keep my firstname as i wanted and remove the rest, i did submit copy of indian passport and birth certificate, (it is always usefull to keep atleast one copy of your indian passport before giving it up for German citizenship) . Friendly lady from Standesamt took all papers and asked me to wait for 1 day until she clears all about changing name, 2nd day she did called me to come by and sign some documents, when i was there she informed me that it is possible to change the name exactly as i wanted and indian names are actually easy to be changed because of some indian consititution etc etc and i could even change my Family name completely if i want to, she even gave me a paper which she copied extra for me just for my knowledge under which rights i have changed my name.
keeping it short, you do have the right to change the name best chance was before applying for german pass and id but since you have already done so you may still change it but might cost you more probably , well i paid 35 Euros for all changes and got a "Bescheinigung" for change of name same time which states my unchanged name and new name, which that "Bescheinigung" i went to apply for new passport and ID and thats it....
PS: My name on Einbürgerungsurkunde will never change but i will get a letter from Rathaus stating and confirming my change of name in their records, actually i dont need to change also on Einbürgerungsurkunde because i can alwasy show this "Bescheinigung" whenever needed.
hope this helps ...
Regards,
N