When I set a point in InRoads, the default annotation is:+elevnorthingeastingstylePt. No.
How can I set it to only display certain objects instead of this entire list?
This is controlled under the Style Manager. When you place a point, you assign a style that determines what a point looks like when it is displayed.
To control what is displayed you would go to Tools > Style manager and edit the style you are using when placing the point.
Once in the Edit Style command, go to the Geometry Feature Folder > Points and you will see the objects that will annotate. If you only want the Point name to display turn off all options except 'Point Name'. You can turn on and off the different options and also control the order they are displayed by changing these settings. Select 'Apply' to save the settings, the 'Apply' the Style Manager. When you go place a new point it should now be using these settings as saved in the Style used for the cogo point.