As long as you are assigning a single variable, you can also use plain assignment in a plpgsql function:
name := (SELECT t.name from test_table t where t.id = x);
Or use SELECT INTO
like @mu already provided.
This works, too:
name := t.name from test_table t where t.id = x;
But better use one of the first two, clearer methods, as @Pavel commented.
I shortened the syntax with a table alias additionally.
Update: I removed my code example and suggest to use IF EXISTS()
instead like provided by @Pavel.