Named CONSTRAINT benefits

There are significant benefits of giving explicit names to your constraints. Just a few examples:

  1. You can drop them by name.
  2. If you use conventions when choosing the name, then you can collect them from meta tables and process them programmatically.

It seems you are using PostgreSQL and there the difference isn't actually that big.

This is because a system generated name in PostgreSQL is actually somewhat meaningful. But "positive_price" is still easier to understand than "foo_price_check":

Think about which error message is better to understand:
new row for relation "foo" violates check constraint "foo_price_check"
or
new row for relation "foo" violates check constraint "positive_price"

In Oracle this is even worse because a system generated does not contain any hint on what was wrong:
ORA-02290: check constraint (SYS_C0024109) violated
vs.
ORA-02290: check constraint (POSITIVE_PRICE) violated


You don't specify RDBMS. the following points apply to SQL Server and I guess quite likely other RDBMSs too.

You need to know the name of the constraint to drop it, also the name of the constraint appears in constraint violation error messages so giving an explicit name can make these more meaningful (SQL Server will auto generate a name for the constraint that tells you nothing about the intent of the constraint).