[BUG REPORT] Impossible to rename object in S3 Bucket without ListAllMyBuckets

I've been searching the web and mostly amazon docs all day and couldn't find an answer to this issue.

I have (root user) several Buckets in AWS S3.

I've assigned a new bucket to a new IAM user and I don't want him to see all the buckets names under: https://s3.console.aws.amazon.com/s3/buckets (He can access his bucket at: https://s3.console.aws.amazon.com/s3/buckets/HISBUCKETNAME)

However, I also want the user to be able to rename file in his bucket. This is impossible if I remove ListAllMyBuckets from his IAM policy.

So in the working user IAM policy I have

{
    "Version": "2012-10-17",
    "Statement": [
        {
            "Effect": "Allow",
            "Action": [
                "s3:ListAllMyBuckets",
                "s3:GetBucketLocation"
            ],
            "Resource": "arn:aws:s3:::*"
        },
        {
            "Effect": "Allow",
            "Action": [
                "s3:*",
                "s3:ListBucket",
                "s3:GetBucketLocation"
            ],
            "Resource": "arn:aws:s3:::bucket-name"
        },
        {
            "Effect": "Allow",
            "Action": [
                "s3:*",
                "s3:PutObject",
                "s3:PutObjectAcl",
                "s3:GetObject",
                "s3:GetObjectAcl",
                "s3:DeleteObject",
                "s3:GetObjectVersion",
                "s3:DeleteObjectVersion"
            ],
            "Resource": "arn:aws:s3:::bucket-name/*"
        }
    ]
}

Unfortunately now the users can see all the buckets in https://s3.console.aws.amazon.com/s3/buckets (though he doesn't have access to them).

Once I remove "s3:ListAllMyBuckets", the user get access denied when trying to rename a file in his bucket.

Is there a way to allow the user to rename a file in his bucket without him having access to the list of all the bucket names (I.E. without ListAllMyBuckets)?

Thanks