Every character (and dragon) has a public profile shown on the
website and via finger <name> in game: tagline, age, origin,
affiliations, background and RP hooks.
Edit yours on the website: open your character's page from
/characters/ and use "Edit profile". There you can also upload
a portrait (large image for the page) and any number of
log icons - small square images used in scene cast lists.
Label icons ("amused", "formal", ...) and pick the fitting one per
scene when finalizing a log.
Org membership (Weyr, Hold, Craft) is shown automatically from the
orgs system - see help org.