There isn’t a specific function that will do this, but it’s definitely something you can add to your site. Personally, I’ve added a custom widget to one of my sites that displays this kind of functionality in the upper-right corner.
Here is some of the code I use:
<?php
$current_user = wp_get_current_user();
$email_hash = md5( $current_user->user_email );
?>
<div class="login_widget">
<?php if ( is_user_logged_in() ) { ?>
<div class="actions">
<ul>
<li class="first-line">Welcome, <?php echo $current_user->display_name; ?>!</li>
<li><a href="https://wordpress.stackexchange.com/questions/44280/<?php echo admin_url("profile.php' ); ?>" title="Profile">Manage Your Profile</a></li>
<li><a href="<?php echo wp_logout_url( home_url() ); ?>" title="Logout">Log Out</a></li>
</ul>
</div>
<img src="http://www.gravatar.com/avatar/<?php echo $email_hash; ?>?s=50" alt="Gravatar" width="50" height="50" />
<?php } else { ?>
<div class="actions">
<ul>
<li class="first-line">
<a href="<?php echo wp_login_url( get_permalink() ); ?>">Log in</a> or
<a href="<?php echo site_url( 'register' ); ?>">join the community</a>
</li>
</ul>
</div>
<?php } ?>
</div>
If the user is logged in, it displays a box like this:
If the user is logged out, it displays a line of text like this: