You can request it. If there is no one else to take over being dad, the court may well be reluctant to disestablish paternity, as courts don't like to deprive a child of a legal father if there is no one to step up and take his place. You really should consult with an attorney on this, and not handle it yourself.
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While you can request the confidenitality by sealing, courts are often reluctant to grant it. But you can certainly try, you never know. However, you can also ask the court that your child only be identified by his/her initial and not full name. There are specific rules and case law regarding sealing court fles and it would be wise to have an attorney assist you. Additionally, as previously pointed out, if there is not another "father" to step in legally, courts are reluctant to grant a disestablishment.
This is meant to be general advise to anyone in your situation and it not meant to create an attorney client relationship.