Obtenga registros para la fecha y hora mínima de cada día de cada persona

SELECT a1.*
FROM accesscards a1
JOIN (SELECT name, MIN(entrydates) mindate
      FROM accesscards
      WHERE name != ''
      GROUP BY name, date(entrydates)) a2
ON a1.name = a2.name AND a1.entrydates = a2.mindate

DEMO