Was there ever a reason given for the name change? I thought at first that it was possibly a mistranslation in the initial episodes. However, in LogueTown Luffy visits a bar named "Gold Roger" and considering the owner knew Gold Roger you'd think they'd get the name right.
There hasn't been any change, I think.
The real and first name is ゴール・D・ ロジャー (Gōru D. Rojā, Gol D. Roger), but he is also known by the name of Gold Roger. I think it's just an in-universe thing.
That said, his real name carries the D. which in the story is being described as "more than a simple initial", often mentioned when talking about The Will of the D:
In the series, few characters have the middle initial "D.". This mysterious middle initial has been called "the Will of D" (Dの意志 - D no Ishi) or "D's will" by several characters in One Piece. [...]
By the way, the meaning for the D. has not been revealed yet, but it certainly holds great importance and is likely to be a major point in the development of the One Piece story.
There is a flash back around the time of the Whitebeard war where Gol. D. Roger is talking to either Whitebeard of the villain form the strong world film.
Here Gol remarks that people have begun calling him gold instead of Gol. D. and laughs about it asking the other person if he wants to know why the "D" is important.
This scene is set 10 years in the past so the name change began around then and slowly spread around the world the way words do. The purpose for the name change appears to be a sign that knowledge of the will of "D" is fading form the world.
One reason of the change of Gol. D. Roger's name to Gold Roger was due to slang. People would rather just connect the name making it Gold Roger than having to say more syllables.
Another reason would be that the treasure One Piece is thought (One Piece isn't confirmed to exist) to contain gold. Since his name's spelling is close to gold, people then just start saying Gold Roger.
In my opinion, his name change would be due to the laziness of the later generations.