Hi,
As I understand, you want to remove the 00:00 timestamp for one day items in calendar view in SharePoint 2013.
If you do not like the timestamp 00:00, you could change time format to 12 hour. You could go to the site setting->
Regional Settings-> time format section.
If you want to remove time stamp, you could add the custom code in the calendar view. For more detailed information, you could refer to the articles below.
The article below is about removing the 12:00 timestamp from Calendar View.
http://weblogs.asp.net/peterbrunone/removing-the-12-00-timestamp-from-calendar-view
The article below is about SharePoint Designer Hide Time in Calendar View.
http://www.codeproject.com/Tips/541676/SharePoint-Designer-Hide-Time-in-Calendar-View
The article below is about removing the time from your SharePoint Calendar.
http://roneiceboggersonsblog.blogspot.com/2013/06/removing-time-from-your-sharepoint.html
There is a similar case:
https://social.technet.microsoft.com/Forums/office/en-US/c3859638-dc3a-4db8-b828-2643be3cee2b/is-there-any-setting-to-avoid-timestamp-from-sharepoint-2013-event-calendar-?forum=sharepointgeneral
Best regards,
Sara Fan