You could do this query:
SELECT 'users' as tbl, count(*) as cnt FROM `users`
WHERE `account_id` = ? AND (`computer_name` = 'name1' OR `computer_name` = 'name2' OR `computer_name` = 'name3')
UNION
SELECT 'users2' as tbl, count(*) as cnt FROM `users2`
WHERE `account_id` = ? AND (`computer_name` = 'name1' OR `computer_name` = 'name2' OR `computer_name` = 'name3')
UNION
SELECT 'users3' as tbl, count(*) as cnt FROM `users3`
WHERE `account_id` = ? AND (`computer_name` = 'name1' OR `computer_name` = 'name2' OR `computer_name` = 'name3')
And then pass the appropriate number of parameters:
$stmt->execute(array_fill(0, 3, $_SESSION['user']['account_id']));