Answer: egosurf

AnswerCrossword Clue
EGOSURF

Google oneself

EGOSURF

Search for oneself on the Web

EGOSURF

Search for yourself on the Web

EGOSURF
Google your own name, e.g.
EGOSURF
Do some searching for oneself
EGOSURFSearch for yourself, in a way
EGOSURFTry to find oneself?