Those identified were then subjected to anti-semitic abuse via social media.
The symbol has been described as a secret signal because punctuation does not show up in ordinary web searches.
Google said that the extension was blocked from its store because it broke its hate speech rules.
The tech giant declined to comment further.
It was called the "coincidence detector" - a reference to a conspiracy theory about Jewish people and global control.
The extension was developed by a far-right group called alt-right.
It had around 2,500 users and a database of 8,800 common Jewish names which it could pick out on websites reported tech site Mic.
The symbol stems from a right-wing group called the Right Stuff, who told Mic it was "a critique of Jewish power".
Jonathan Weisman, deputy Washington editor of the New York Times, wrote about his experience of receiving a tweet with his name wrapped around with brackets.
When he asked what it meant the tweeter replied that he was "belling the cat".
"The anti-Semitic hate hasn't stopped since," wrote Mr Weisman, who has now altered his name on Twitter to include the brackets himself. Others are doing the same in support.
"Nobody's telling us to self-identify. We are showing strength and fearlessness," he tweeted in response to a journalist who said it made her uncomfortable.
He also said that much of the hate appeared to come with "self-identified Donald J Trump supporters" - and many had Twitter names which included the US presidential candidate's name.
Google has banned an extension of its Chrome browser which was being used to identify Jewish names on the internet by surrounding them with three sets of brackets, or parentheses.