Renaming a column in a PostgreSQL database table
You could try it yourself as well, but no: renaming a column won't break your foreign keys.

Try this:

CREATE TABLE a (a_id serial PRIMARY KEY);

CREATE TABLE b (a_id integer REFERENCES a (a_id));

ALTER TABLE a RENAME COLUMN a_id TO id;


and have a look at b's definition.

Imagine the world if it weren't so: every single column renaming (in my experience happening a lot in the first phases of development) would involve modifying constraints here and there.  Wouldn't make much sense, would it?

Doing this in a dump is rather error-prone, I would not do that.