wp_register displays logged in user as “Site Admin” apposed to Logged in user

I’m just working on a little hobby word-press site I have;

<?php wp_loginout(''); ?>
<?php wp_register( '',''); ?>
In the top rite corner of my site, <?php wp_loginout(''); ?> works great however <?php wp_register( '',''); ?> when logged in always shows logged in user as “Site Admin” is there a universal variable I can use or something to just show the logged in users name.

Note: I am using (”,”) for the wp_register parameters so it isn’t displayed in li format.

Thanks

Ben