Initial observation
In this hypothetical example, two platforms show the same username. This is a string match. It does not yet establish whether the profiles belong to one person, different people or a project.
Checking the connection
Look for an explicit link to the second profile in a known source. Even mutual references need a time and content context. A shared avatar is an observation, not independent proof.
Recording the outcome
Distinguish a sourced link from visual similarity. If there is no explicit connection, state that. Do not transfer personal details between profiles solely because of a username.