Я бы предложил такой вариант:
<?php
$board = [
'a' => [
'1' => '',
'2' => '',
'3' => '',
'4' => '',
'5' => '',
'6' => '',
'7' => '',
'8' => '',
],
'b' => [
'1' => 'белый конь',
'2' => '',
'3' => '',
'4' => '',
'5' => '',
'6' => '',
'7' => '',
'8' => '',
],
// ---
'g' => [
'1' => '',
'2' => '',
'3' => '',
'4' => '',
'5' => '',
'6' => '',
'7' => '',
'8' => '',
],
'h' => [
'1' => '',
'2' => '',
'3' => '',
'4' => '',
'5' => '',
'6' => '',
'7' => '',
'8' => '',
]
];
// ход конем b1 -> a3
$board['a']['3'] = 'белый конь';
$board['b']['1'] = '';
print_r($board);
PHP chess board