"namesearch" is internet slang meaning to search for a person's name (particularly one's own) on a social media platform for the purpose of obsessively reading and engaging with posts containing it. It travels through TikTok, Discord, Twitter/X, gaming chat and group DMs, and most teens absorb it from feeds and memes rather than from face-to-face friends. Using it is normal online-native behaviour and does not on its own indicate anything worrying. If you are not sure what they mean, asking them to explain it is a friendly, low-stakes way in; teens generally enjoy translating their corner of the internet for a curious parent.