What sharing a surname does not prove
Same-character surnames can create a sense of connection, but they are not evidence of close kinship.
What the match does show
Two people writing 李 share a written surname. That is the limited observation. It does not by itself show a common recent ancestor, a place of origin, a generation character, or a relation to any famous Li. Romanized spellings are even less specific because different Chinese characters can share a pronunciation.
How to speak accurately
Prefer “this surname is associated with…” over “this family descends from…”. Individual genealogy requires family records and historical research beyond a naming tool. The distinction matters especially for surnames connected with emperors, scholars, or well-known leaders.
Li Yuan’s 李 is a historical example; a new user selecting 李 is not thereby part of his lineage.
What to do with this
Choose a surname because its sound, form, and context suit you, not as a claim to another family’s history.
Sources & limits
Sources support the specific facts cited above. An editorial name interpretation is not an ancient quotation or proof of family ancestry.