To quote from the Wikipedia entry:
[Leatherface] was originally portrayed by Gunnar Hansen. His real
name is unknown, although older brother Chop Top calls him "Bubba" in
the second movie and in Texas Chainsaw 3D, his name is Jedidiah. While
Chop Top is most likely using this colloquial word for "brother"
affectionately, it is possible that "Bubba" is Leatherface's proper
name. In the latter case, assuming that his surname is Sawyer as with
his older brothers, his full name would be Bubba Sawyer. In the third
film he is only referred to as Junior by his family with his first
name not being stated. In the fourth film Leatherface is called
"Leather" by his relatives.
This therefore leaves two names: Bubba Sawyer and Jedidiah Sawyer.
Again from the Wikipedia entry:
In the remake series, Leatherface is named Thomas and lives with his
adoptive family, the murderous Hewitts, he is portrayed by Andrew
Bryniarski. In this series his family never refers to him as
Leatherface, but by his real name.
This adds a third name, Thomas Hewitt.
So now we have three total names for him, the real question is why the name change. I haven't found anything quoting any of the directors, but there are a few logical leaps that can be made. The original movie was marketed as being a true story. It wasn't. But clever marketing made the event seem even scarier and drew in bigger crowds.
It certainly seems plausible that in the reboot of the series the makers simply wanted to "freshen" things up and introduce a new name to bring a new generation of film-goers into the story. A quick browse through sites like Yahoo Answers and the like shows many people asking if the new name, Hewitt, is based off a real-life family.
Therefore, I'd have to conclude that the only reason for the name change was to keep the series fresh and to get a new generation of viewers to question whether this new family were real (now that many realise the original family were not).
However, I will hold my hands up and say I have no citable source from a director/producer to corroborate that - it's just an educated guess.