ALTER CONVERSION changes the definition of a conversion.
You must own the conversion to use ALTER CONVERSION. To alter the owner, you must also be a direct or indirect member of the new owning role, and that role must have CREATE privilege on the conversion's schema. (These restrictions enforce that altering the owner doesn't do anything you couldn't do by dropping and recreating the conversion. However, a superuser can alter ownership of any conversion anyway.)
The name (optionally schema-qualified) of an existing conversion.
The new name of the conversion.
The new owner of the conversion.
To rename the conversion iso_8859_1_to_utf8 to latin1_to_unicode:
ALTER CONVERSION iso_8859_1_to_utf8 RENAME TO latin1_to_unicode;
To change the owner of the conversion iso_8859_1_to_utf8 to joe:
ALTER CONVERSION iso_8859_1_to_utf8 OWNER TO joe;