If there are more than 1 FBA sellers on the listing, then there's a good chance it is NOT a private label product.
Most private label products on Amazon will only have one New FBA seller on the listing and the Name of the seller will be the same as the name of the brand on the listing.
If you are concerned about the product being a private label, you can 1. ask your supplier for an authorization letter from the brand stating that you can sell on Amazon and/or 2. You could also try to reach out to the brand and they should be able to let you know as well.