Making custom field’s ‘Name’ available in the dropdown list by default in a theme?

your best option is to create a custom meta box with-in your theme and then the user will have it no matter if he typed it once before.

// Hook into WordPress
add_action( 'admin_init', 'add_custom_metabox' );
add_action( 'save_post', 'save_custom_intro_image' );

/**
 * Add meta box
 */
function add_custom_metabox() {
    add_meta_box( 'custom-metabox', __( 'Intro Image' ), 'intro_image_custom_metabox', 'post', 'side', 'high' );
}

/**
 * Display the metabox
 */
function intro_image_custom_metabox() {
    global $post;
    $introimage = get_post_meta( $post->ID, 'intro_image', true );
        ?>
    <p><label for="intro_image">Intro Image:<br />
        <input id="siteurl" size="37" name="intro_image" value="<?php if( $introimage ) { echo $introimage; } ?>" /></label></p>
    <?php
}

/**
 * Process the custom metabox fields
 */
function save_custom_intro_image( $post_id ) {
    global $post;   

    if( $_POST ) {
        update_post_meta( $post->ID, 'intro_image', $_POST['intro_image'] );
    }
}

Hope This Helps