Are PostgreSQL column names case-sensitive?

Identifiers (including column names) that are not double-quoted are folded to lowercase in PostgreSQL. Column names that were created with double-quotes and thereby retained uppercase letters (and/or other syntax violations) have to be double-quoted for the rest of their life:

"first_Name"

Values (string literals / constants) are enclosed in single quotes:

'xyz'

So, yes, PostgreSQL column names are case-sensitive (when double-quoted):

SELECT * FROM persons WHERE "first_Name" = 'xyz';

Read the manual on identifiers here.

My standing advice is to use legal, lower-case names exclusively so double-quoting is not needed.

To quote the documentation:

Key words and unquoted identifiers are case insensitive. Therefore:

UPDATE MY_TABLE SET A = 5;

can equivalently be written as:

uPDaTE my_TabLE SeT a = 5;

You could also write it using quoted identifiers:

UPDATE "my_table" SET "a" = 5;

Quoting an identifier makes it case-sensitive, whereas unquoted names are always folded to lower case (unlike the SQL standard where unquoted names are folded to upper case). For example, the identifiers FOO, foo, and "foo" are considered the same by PostgreSQL, but "Foo" and "FOO" are different from these three and each other.

If you want to write portable applications you are advised to always quote a particular name or never quote it.