The move came after Labour expressed concern that allowing comments from unnamed people would allow the process to be rigged.
The government has now said anonymous responses will ...
... not form part of the final analysis of the consultation.
Ministers said anonymous submissions made up 3.5% of the total received.
The SNP government's minister for government strategy, Bruce Crawford, previously said respondents to the consultation could indicate their wish to remain anonymous, while responses which did not include personal information would also be treated as anonymous.
Scottish Labour's deputy leader, Anas Sarwar, said anonymous responses meant the consultation was not only "open to abuse but designed for abuse".
At the weekend, the government said an independent analysis of its consultation would identify any multiple identical responses - anonymous or otherwise.
But ministers have now said that, "in order to prevent significant numbers of anonymous responses, given the media coverage generated about the issue, responses will only be accepted and included in the analysis if they provide personal identification details".
The government said duplicate identical responses sent from the same computer would also be excluded.
At the same time, Mr Crawford said 414 consultation responses out of a total of 11,986 received so far were anonymous.
'Humiliating climbdown'
He said: "As the figures we have published demonstrate, there is absolutely no evidence of anonymous responses skewing the process - quite the reverse - but we can and will make the process stronger still by requiring all submissions to have personal identification details before they are taken into account.
"While anonymous contributions would always have been separately identified, we will now ensure that no anonymous submissions are included in the analysis at all.
"And while there is no evidence of duplicate identical responses from the same person, we can and will ensure that any received are also excluded from the independent analysis so that their view is only represented once."
A Scottish Labour spokesman said: "This is a humiliating climbdown for the SNP government, which appears to have lost control over its own consultation and now appears to be making it up as it goes along.
"It is only appropriate the Scottish government now strip out the anonymous submissions and we welcome the belated acceptance that this process is flawed and open to abuse."
The Scottish government consultation will run until May, while a similar exercise by UK ministers has formally closed.
The SNP has set autumn 2014 as its preferred date for the referendum.
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