"I wanted to know if the was any consequences for having not his real name?"
But what exactly do you mean by "real" name?
Was this the name he was using while you were in a relationship with him?
If that is the case (unless he's an undercover police officer or MI5 agent etc - and that's not a joke, they did get involved with women they were investigating) then that is likely not going to go anywhere if you want to get his parental responsibility removed.
If you were to try to do that then he would just need to do a DNA test to show that he was the father.
@Youcancallmeirrelevant
"... if he used a different name on the birth certificate that is weird."
Not really, it's common place for married women who take their husband's name to do that.
Why would a man do that though?
One reason may be because he has a criminal record under his old name.
Many companies refuse to employ people with any sort of criminal record at all. For example, if you wish to work for Amazon in one of their fulfillment centres (these are the people who pick and pack the stuff you've ordered) then you'll never get a permanent job with them if you have a criminal record of any sort.
Just as an aside, the basic wage at Amazon is £13.50 per hour or £26,325 for a typical 37.5 week. So, if you have a criminal conviction it can be a problem getting a job paying £26k a year.
[EDIT]
That is, until the Rehabilitation of Offenders Act kicks in when people are no longer required to disclose their convictions