Answer: egosurf

AnswerCrossword Clue
EGOSURFGoogle oneself
EGOSURFSearch for oneself on the Web
EGOSURFSearch for yourself on the Web
EGOSURFGoogle your own name, e.g.
EGOSURFDo some searching for oneself
EGOSURFSearch for yourself, in a way
EGOSURFTry to find oneself?