partial class Examples
{
  public static Result RenameObject(RhinoDoc doc)
  {
    ObjRef obj_ref;
    var rc = RhinoGet.GetOneObject("Select object to change name", true, ObjectType.AnyObject, out obj_ref);
    if (rc != Result.Success)
      return rc;
    var rhino_object = obj_ref.Object();

    var new_object_name = "";
    rc = RhinoGet.GetString("New object name", true, ref new_object_name);
    if (rc != Result.Success)
      return rc;
    if (string.IsNullOrWhiteSpace(new_object_name))
      return Result.Nothing;

    if (rhino_object.Name != new_object_name)
    {
      rhino_object.Attributes.Name = new_object_name;
      rhino_object.CommitChanges();
    }

    return Result.Success;
  }
}

import rhinoscriptsyntax as rs

obj_id = rs.GetObject("Select object to change name")
object_new_name = rs.GetString("New object name")

rs.ObjectName(obj_id, object_new_name)