You cannot lie about your marital status. It is an important factor for purposes of taxes, employment and possibly your former spouse. Look at your Judgment for Dissolution of Marriage and your parenting agreement. You may be obligated to tell your ex., especially if your remarriage affects child support or visitation. If there is no mention in those documents and support or visitation are no affected, then you are not obligated to tell your ex but your children most certainly will speak of it. Your new marriage will be public record but it is very rare that anyone every looks at those records unless there is a very specific reason to do so. For best guidance, you should speak in privacy with a lawyer where you can reveal all your details in a confidential situation.
CAVEAT: The above assumes that you are not hiding your remarriage because your new spouse is a convicted felon or a sex offender required to register that status.
Sign up to receive a 10-part series of useful information and legal advice about the divorce process.