The statement that names of schema objects are unique isn't strictly true, just mostly true. Take the case of a unique constraints.

Concerning CONSTRAINTS you are right. Constraints seems to be an exception:

• Their name belongs to a schema, but are not necessarily unique within this context: https://www.postgresql.org/docs/current/catalog-pg-constraint.html.
• There is a UNIQUE index within the system catalog pg_constraints:  "pg_constraint_conrelid_contypid_conname_index" UNIQUE, btree (conrelid, contypid, conname), which expresses that names are unique within the context of a table/constraint-type. Nevertheless tests have shown that some stronger restrictions exists across table-boarders (,which seems to be implemented in CREATE statements - or as a consequence of your mentioned correlation between constraint and index ?).
  

I hope that there are no more such exception to the global rule 'object names in a schema are unique': https://www.postgresql.org/docs/current/sql-createschema.html

This facts must be mentioned as a short note in glossary and in more detail in the later patch about the architecture.

J. Purtz