How can I get taxonomy term name using term slug & post ID using build in WordPress function or class?

This can be done in multiple different ways. Depending on the context, one way may be better than the other ways.

Using WP_Term_Query class:

Most wp_term related queries are internally done using the WP_Term_Query class. So if you need different options, using this class can be very useful. For example:

// all of these arguments are optional
$args = array(
    // object_ids can be a single post id or array of post ids
    'object_ids' => get_the_ID(),
    // taxonomy can be just a single taxonomy string or array of taxonomies
    'taxonomy' => array( 'category', 'post_tag' ),
    // if you need only a specific slug
    'slug'  => 'your-slug-here'
);
$term_query = new WP_Term_Query( $args );
foreach( $term_query->get_terms() as $term ) {
    echo "{$term->name} ({$term->taxonomy})";
}

Using get_the_terms function:

For theme template files (e.g. single.php), get_the_terms() function may be more appropriate. It internally uses cache functions, so it’s probably more efficient in this context. For example:

$terms = get_the_terms( get_the_ID(), 'post_tag' );

if( $terms ) {
    $term = wp_list_pluck( $terms, 'name', 'slug' );
    if( isset( $term['some-post-tag'] ) ) 
        echo '<h1>' . $term['some-post-tag'] . '</h1>';
    else 
        echo '<h1>No tag found with [some-post-tag]</h1>';
}

For this implementation, wp_list_pluck() function may be useful, since get_the_terms() doesn’t support slug directly.

Using get_term_by function:

Since each WordPress taxonomy term slug is unique, so basically if you know the slug from some other source, then post ID may not be needed at all. In this case, you may use the get_term_by function. For example:

// $terms = get_term_by( 'slug', 'some-category-slug', 'category' );
$terms = get_term_by( 'slug', 'some-post-tag', 'post_tag' );
if( $terms ) {
    echo $terms->name;
}

get_term_by function doesn’t support post ID, but as I said, you may not need post ID at all.