name_taken, or the store’s own name resolution finds it (slug, name,
or a launched agent’s instance name): every name a fork could take is
checked against both, automatic or typed (#4746).
Whether a user agent (not a seeded template) already goes by name,
case-insensitively: as its name, or as its branch label, which is what a
renamed fork shows. Names are unique among user agents: the picker lists
them by name, and name-keyed registrations collide otherwise. A launched
agent’s instance name is the store’s to check (agents_matching_name).