Retrieve Names of Check Constraints Specific to a Column
how can I select all of the check constraints associated with that column?

pg_constraint.conkey is an array column, so we join on a.attnum = ANY(c.conkey) and the oid of the relation additionally. Like:
SELECT conname -- pg_get_constraintdef(oid), *
FROM   pg_constraint c
JOIN   pg_attribute  a ON a.attrelid = c.conrelid     -- !
                      AND a.attnum   = ANY(c.conkey)  -- !
WHERE  c.conrelid = 'hypothetical_table'::regclass
AND    c.contype = 'c'  -- c = check constraint
AND    a.attname = 'some_col';

But I am doubtful of your overall objective:

When I rename a column in a table, I would like to dynamically rename the matching check constraints as well.

CHECK constraints are always table constraints in Postgres and can reference any number of table columns. Even when formulated as column constraints! The manual:

Column Check Constraints
The SQL standard says that CHECK column constraints can only refer
to the column they apply to; only CHECK table constraints can refer
to multiple columns. PostgreSQL does not enforce this restriction; it
treats column and table check constraints alike.

So some_col and some_col_also can be referenced at the same time (multiple times). And both can be in the constraint name. I don't see how a completely dynamic solution can be bullet-proof, unless you can rely on a strict naming convention. (Can you really?). Is the following a reference to some_col or some_col_also?
some_col_also_is_a_fruit  -- oh, wait!

Rewriting the constraint expression itself also demands attention.