When I changed my legal name here in South Dakota, I challenged the requirement to post a Notice of Hearing in the local paper. It shows the old name and the new name and must be published once per week for four weeks. Not very private.
I was told that the reason is to prevent identity theft, people dodging warrants or child support, or maybe they are listed as a Sex Offender. The date of the hearing is published so that anyone wishing to challenge the name change, (for any of those reasons), can appear in court and present the challenge to the judge. Since it is a hearing, the petitioner has the opportunity to provide the court with an explanation. All of this is done in a public hearing and becomes a part of the public record.
I have heard of people requesting the record be sealed, but I don't see any reason to do that. Once I had the court order there was nothing anyone could do about anyway.