Display max value individual by day

Anonymous 

Try below DAX in a calculated column

MaxBreak =
VAR __maxTime =
    MAXX (
        FILTER (
            'Table',
            'Table'[Date] = EARLIER ( 'Table'[Date] )
                && 'Table'[Name] = EARLIER ( 'Table'[Name] )
        ),
        'Table'[Break time]
    )
VAR __result =
    IF ( 'Table'[Break time] = __maxTime, __maxTime, BLANK () )
RETURN
    __result

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Anonymous , Try like

if([break time] =maxx(filter(table, [name]=earlier([name]) && [date]=earlier([date])),[break time]) ,[break time],blank())

Anonymous 

Try this as measure:

Measure = 
VAR BT =  
CALCULATE(
    MAX('Table'[Break time           ]),
    ALLEXCEPT('Table', 'Table'[Name        ],'Table'[Date          ]))

RETURN

IF( BT = MAX('Table'[Break time           ]),FORMAT(BT,"hh:mm"),"")

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