Make Spot Heights High and Low
You need the spatial analyst. SA does lack some basic tools, so you will need to determine what you want to classifiy as a 'peak'
- The single highest value?
- A range of high values? as an area?
- As a neighborhood difference in elevation (ie difference in elevation within 1km^2 with a difference in elevation of 500m
The first option requires that you know what the highest value is http://pro.arcgis.com/en/pro-app/tool-reference/data-management/get-raster-properties.htm then you simply query the dem for it. Pretty useless since it will miss out 'peaks' that are 1 meter shorter
The second option is a bit more forgiving, except plateaus at elevation (mesas) would be considered peaks
The third option entails using an appropriate neighborhood with focal statistics or block statistics with 'range' option
http://pro.arcgis.com/en/pro-app/tool-reference/spatial-analyst/focal-statistics.htm
The options are not limited to the above, but they are starting points and can be used in combination. Of course all are way slower than taking your mouse and clicking points on a map 
ie humanware
