I don't know if this is the correct solution, but giving ListAllMyBuckets permission worked for me.

I just added another statement along with the previous one.

{
    "Sid": "Stmt1490288788",
    "Effect": "Allow",
    "Action": [
        "s3:*"
    ],
    "Resource": [
        "arn:aws:s3:::bucket-name/*"
    ]
}{
    "Sid": "Stmt1490289746001",
    "Effect": "Allow",
    "Action": [
       "s3:ListAllMyBuckets"
    ],
    "Resource": [
       "arn:aws:s3:::*"
    ]
}

So this policy lists all the buckets, but only allow put/delete/get access to the specific bucket. Still wondering what's the relation between rename/copy & list all bucket permissions.

While there isn't actually rename functionality in S3 itself, some interfaces may try and implement it by using S3 PUT object copy and DELETE actions behind the scenes. Their implementation may require other bucket-level permissions to complete, which is why it may be failing with your policy. Try this:

{
    "Sid": "Stmt1490288788",
    "Effect": "Allow",
    "Action": [
        "s3:*"
    ],
    "Resource": [
        "arn:aws:s3:::bucket-name",
        "arn:aws:s3:::bucket-name/*"
    ]
}

The difference being this grants permissions to actions performed on the bucket itself (the first resource declared), as well as the objects in the bucket (the second resource declared).