How did you create the table and the index? Does the index really index the "name" column? This works for me: 
#!/usr/bin/perl
use warnings;
use strict;

use DBI;

unlink 'test.db' or warn $!;

my $dbh = DBI->connect('dbi:SQLite:test.db', q(), q());
$dbh->do(q(create table profile (profile_id integer, name varchar)));
$dbh->do(q(create index idx_name on profile (name, profile_id)));
my $insert = $dbh->prepare(q(insert into profile values(?, ?)));
$insert->execute(@$_) for [10, 'Joseph'],
                          [11, 'William'],
                          [12, 'Elisabeth'];

my $sql    = q{ SELECT profile_id FROM profile INDEXED BY idx_name
                WHERE name == ? };
my $sth    = $dbh->prepare($sql);
my $name   = 'William';

$sth->execute($name);
my $arr = $sth->fetchall_arrayref;
print "@$_\n" for @$arr;

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If I switch name and profile_id in the index creation, I get the error you mentioned, but only if no other index has been yet defined. I am not sure this is the intended behaviour.
لսႽ† ᥲᥒ⚪⟊Ⴙᘓᖇ Ꮅᘓᖇ⎱ Ⴙᥲ𝇋ƙᘓᖇ

In reply to Re: "Can't use index" with DBD::SQLite by choroba
in thread "Cannot use index" with DBD::SQLite by LonelyPilgrim

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