Return Boolean Value as TRUE or FALSE in Select (PostgreSQL/pgAdmin)

A simple cast to text will do the job (unless you need upper case spelling):

SELECT true::text AS t, false::text AS f;

 t    | f
------+-------
 true | false

Else, the text representation depends on library and client you use to connect. JDBC for instance renders boolean values as 'true' / 'false' anyway:

db<>fiddle here
_{Old sqlfiddle}

You will love this change in Postgres 9.5 (quoting the release notes):

• Use assignment cast behavior for data type conversions in PL/pgSQL assignments, rather than converting to and from text (Tom Lane)

This change causes conversions of Booleans to strings to produce true or false, not t or f. Other type conversions may succeed in more cases than before; for example, assigning a numeric value 3.9 to an integer variable will now assign 4 rather than failing. If no assignment-grade cast is defined for the particular source and destination types, PL/pgSQL will fall back to its old I/O conversion behavior.

Bold emphasis mine.

If all you want to show is the literal TRUE or FALSE, you can use the case statements like you had proposed. Since PostgreSQL treats TRUE, true, yes, on, y, t and 1 as true, I'd control how I'd want the output to look like.

Where clause can be written like:

select * from tablename where active
--or--
select * from tablename where active = true

(My recommendation is the same as PostgreSQL - use true)

When selecting, although there may be hesitation to use the case statements, I'd still recommend doing that to have control over your output string literal.

Your query would look like this:

select 
  case when active = TRUE then 'TRUE' else 'FALSE' end as active_status,
  ...other columns...
from tablename
where active = TRUE;

SQLFiddle example: http://sqlfiddle.com/#!15/4764d/1

create table test (id int, fullname varchar(100), active boolean);
insert into test values (1, 'test1', FALSE), (2, 'test2', TRUE), (3, 'test3', TRUE);

select
  id,
  fullname,
  case when active = TRUE then 'TRUE' else 'FALSE' end as active_status
from test;

| id | fullname | active_status |
|----|----------|---------------|
|  1 |    test1 |         FALSE |
|  2 |    test2 |          TRUE |
|  3 |    test3 |          TRUE |