df.groupby([df.Time.str[0:13], 'Type']).Name.value_counts()
# or
df.groupby([df.Time.str[0:13], 'Type', 'Name']).size()

Time           Type                      Name
2018-04-07 15  COMMUNICATIONS ALARM      Device Management IP is Unreachable    141
2018-04-07 16  COMMUNICATIONS ALARM      Device Management IP is Unreachable     64
2018-04-07 17  COMMUNICATIONS ALARM      Device Management IP is Unreachable      6
...
2018-04-09 14  COMMUNICATIONS ALARM      Device Management IP is Unreachable      8
2018-04-09 15  COMMUNICATIONS ALARM      Device Management IP is Unreachable     11
2018-04-09 16  COMMUNICATIONS ALARM      Device Management IP is Unreachable      5
2018-04-09 17  QUALITY_OF_SERVICE_ALARM  Temperature Absolute High               64
                                         Memory Absolute High                     1