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You can use the below hook in your child theme’s functions.php in order to change the billing section name.

function wc_billing_field_strings( $translated_text, $text, $domain ) {
switch ( $translated_text ) {
case 'Billing details' :
 $translated_text = __( 'New_Section_Name', 'woocommerce' );
break;
}
return $translated_text;
}
add_filter( 'gettext', 'wc_billing_field_strings', 20, 3 );

Please replace the New_Section_Name with your section name.

Thank you!