public void SetName( 
   string attachmentName
)

public async Task UpdatingAttachments()
{
    await ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
    {
        using (Geodatabase geodatabase = new Geodatabase(new DatabaseConnectionFile(new Uri("path\\to\\sde\\file\\sdefile.sde"))))
        using (FeatureClass landUseCaseFeatureClass = geodatabase.OpenDataset<FeatureClass>("LocalGovernment.GDB.LandUseCase"))
        {
            QueryFilter filter = new QueryFilter { WhereClause = "CASETYPE = 'Rezoning'" };

            using (RowCursor landUseCursor = landUseCaseFeatureClass.Search(filter, false))
            {
                while (landUseCursor.MoveNext())
                {
                    using (Feature rezoningUseCase = (Feature)landUseCursor.Current)
                    {
                        IReadOnlyList<Attachment> rezoningAttachments = rezoningUseCase.GetAttachments();
                        IEnumerable<Attachment> filteredAttachments = rezoningAttachments.Where(attachment => !attachment.GetName().Contains("rezoning"));

                        foreach (Attachment attachmentToUpdate in filteredAttachments)
                        {
                            attachmentToUpdate.SetName(attachmentToUpdate.GetName().Replace(".pdf", "Rezoning.pdf"));
                            rezoningUseCase.UpdateAttachment(attachmentToUpdate);
                        }
                    }
                }
            }
        }
    });
}