According to Esri documentation it's safe to rename a GIS Server machine name in your ArcGIS site. ArcGIS Server will detect the change and update it automatically.
Common problems and solutions—Documentation (10.4) | ArcGIS Enterprise
I would like to know if this applies to the ArcGIS Data Store. If I change the machine name of my Data Store machine, will that change be automatically detected and will my Data Store continue to work?