ego-surfing
US /ˈiːɡoʊˌsɜːrfɪŋ/
UK /ˈiːɡoʊˌsɜːrfɪŋ/

1.
the practice of searching for one's own name on the Internet
:
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He spends hours every day ego-surfing to see what people are saying about him.
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Ego-surfing can be a harmless pastime, but it can also lead to obsession.
1.
the act of searching for one's own name on the Internet
:
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She admitted to ego-surfing occasionally, just to keep up with her online presence.