If the data is brought into GIS as a feature class, one can create fields and populate the coordinates for the coordinate system of your choice using Calculate Geometry.
The Calculate Geometry tool allows you to access the geometry of the features in a layer. The tool can calculate coordinate values, lengths, and areas, depending on the geometry of the input layer. You can only calculate the area, length, or perimeter of features if the coordinate system being used is projected. Keep in mind that different projections have different spatial properties and distortions. If the coordinate system of the data source and data frame are not the same, you may get a different result if you calculate geometry using the data frame's coordinate system than when you calculate using the data source's coordinate system.
Calculating area, length, and other geometric properties—Help | ArcGIS for Desktop
Alternately, one could use XTools Pro, a third-party software that fits into ArcGIS Desktop. It has an "Add XYZ Coordinates" function (under Table Operations) that works in a similar manner, but does both X and Y at the same time.
https://xtools.pro/en/overview/
Chris Donohue, GIS