Correct reply is a comment from Anton Kovalenko
You cannot use variable as table or column name in embedded SQL ever.
UPDATE dynamic_table_name SET ....
PostgreSQL uses a prepared and saved plans for embedded SQL, and references to a target objects (tables) are deep and hard encoded in plans - a some characteristics has significant impact on plans - for one table can be used index, for other not. Query planning is relatively slow, so PostgreSQL doesn't try it transparently (without few exceptions).
You should to use a dynamic SQL - a one purpose is using for similar situations. You generate a new SQL string always and plans are not saved
DO $$
DECLARE r record;
BEGIN
FOR r IN SELECT table_name
FROM information_schema.tables
WHERE table_catalog = 'public'
LOOP
EXECUTE format('UPDATE %I SET id = 10 WHERE id = 15', r.table_name);
END LOOP;
END $$;
Attention: Dynamic SQL is unsafe (there is a SQL injection risks) without parameter sanitization. I used a function "format" for it. Other way is using "quote_ident" function.
EXECUTE 'UPDATE ' || quote_ident(r.table_name) || 'SET ...