If you have the name and address for the year of the census and cannot find the person they may have been missed from the census,the name may have been mistranscribed,if its the 1911 census the head of the household would have filled it in, anyone that was away from the address on that date would not have been on their form,but should have been on the census form wherever they were staying!Its not that unusual for people to have benn missed.
If you don't want to post the persons details here you can send me a private message and I will take a look at the census for you.
Also I think that not all of the 1911 census is fully transcribed yet.
If its not a census year you were looking for try electoral rolls.
Not sure about the birth cert being changed,is it possible that mother remarried and her new husband adopted the child?