Yes as Peter says, please update your zip code to a geographical role of zip code:
Please note that Tableau will map out the AREA part of the zip code. Not to the street level.
Next, on a blank worksheet, bring your zip code field into the centre of the canvas, where you'll find the rows and columns will be auto populated with latitude and longitude. Then bring your name field into colour on the marks card, right click on this and change it to a measure by using count or count distinct.
You should then get this kind of view:
Have attached the workbook for you to see how it works.
Map_v10.2.twbx 7.6 MB