I have two polygons that delineate two site boundaries. I have a bunch of point features inside the polygons. Is there a way to create a attribute that indicates what polygon boundary the point feature is located in?

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You can use the Spatial Join tool with the points as the target features and the polygons as the join features. You should leave the keep all target features option checked if you want to include all points in the output, even if some fall outside of any of the polygons. If you want the output to include the polygon object ID in a JoinFID field you should change the Join Operation from One To One to One to Many. However, be aware that the One To Many option will duplicate any points that fall exactly on a shared boundary of the polygons. By default the attributes of both the points and the polygons will be included in the output, which are fully preserved under the One to Many option or summary values (typically First or Sum by default) when the One to One option is chosen. The tool also allows you to optionally adjust the field map.

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