There are definitely some name changes that take place.
Greg Lippmann became Jared Vennett (played by Ryan Gosling).
Steve Eisman became Mark Baum (played by Steve Carrell).
Ben Hockett became Ben Rickert (played by Brad Pitt).
Michael Burry, played by Christian Bale does not have his name changed.
Otherwise, the various linked articles show a lot of interview material which shows the various characters are quite similar to their real-life counterparts.
For example, Michael Lewis, the author of the book, said the following in an interview with Vulture:
The hair. The hair is their hair. I was shocked by how close,
especially the principals, captured the actual people. Christian Bale
was so much like Michael Burry that I thought it was creepy — he did a
very, very good job. He was wearing Michael Burry’s clothes. That
T-shirt and shorts. I asked Adam: How did he even know he was wearing
that when I went to see him? The answer is he didn’t. That’s what
Michael Burry was wearing when Christian Bale went to see him, and
Christian was like, “Can I have your clothes?” I guess he has had to
get new clothes now.
McKay, the director and co-writer, commented:
“The real people have been the biggest challenge,” says McKay, who had
the duller job of fielding individual complaints: Why do I have to be
talking about my balls? Does he have to refer to me as a dick? McKay
had made some concessions: He’d changed Lippmann’s name — the
character is now called Jared Vennett (“I pronounce it Ven-AY,” said
Gosling) — and the last names of three attention-shy traders from
Cornwall Capital. The biggest change was Steve Eisman’s character: In
the book, Lewis reveals that Eisman lost a young child, which gives
his character a necessary pathos, but Eisman didn’t want it in the
film, so McKay replaced it with something else, and the character
became “Mark Baum.” This didn’t prevent Eisman from coming to the set
and advising Steve Carell on how to be a better him. “It’s, you know …
interesting to have the person you are playing show up the first or
second day you are shooting,” said Carell, who was roaming around the
set in an uncannily Eismanesque hairpiece between takes. “It’s a
little daunting to have the person staring at you. And offering
So, it appears a mixture of hiding the real people at their requests, and hiding parts of their life at their request led to the name changes (although, as the article states, despite the name change Eisman still advised Carrell on how to "play him".