This has been left intentionally unclear and mysterious. Jon Watts, the director, was asked this question directly and left it up for the viewer to decide what they felt was right.
Interestingly he does state "he was able to mask himself and his background and change all of that". Now the two parts here, "mask his background" and "change all of that" are in contention. So he could have masked his background so it was hard for people to find out about a Quentin Beck who used to work for Stark Industries or he changed it and came up with a new name.
IGN: Is Quentin Beck actually his name, or is that a fake name? Because we were like, "How to no one check up on this guy and not notice that he worked for Tony?"
Watts: Some of these are deleted scenes as well, but you have to think that, in addition to all this technology he was using, that there was a way that he was able to mask himself and his background and change all of that. So, I think what's good about Mysterio that it doesn't all remain mysterious. There's a lot of questions at the end of the movie that are part of what makes Mysterio fun.
IGN: And, so I'm not mischaracterizing you, are you saying it's a deleted scene of kind of getting into how he's masking his identity?
Watts: There's a little bit more of like seeing behind the scenes of how they put everything together. But, it's just things that didn't make it for time. I want to see how people interpret it and see if people come up with what we can offer.
IGN, Spider-Man: Far From Home Director Jon Watts Answers All Our Biggest Questions
Looking into the sentence used in the question by Mysterio himself the "named Quentin" part is totally redundant if he is talking about himself. I don't think we can infer too much from this but it does lend credence to this not being his own name.
If we look into the flashback of Beck when he was working for Stark Industries we only ever see him in a black suit with no name badge so that isn't overly helpful.
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The deleted scene Jon references above, if I'm looking right, is with Beck and his team in London. It shows them instructing people to film what happens and then making the fake shockwave. It then shows us Fury calling and his response to it and how good of an actor Beck is. Unfortunately, though this is just about how they got the whole plan to work but shows nothing of his backstory.