To completely remove the Blogroll title from WordPress follow these simple instructions. These steps will remove the BlogRoll Title from your WordPress theme; the actual BlogRoll will still show as normal.
NOTE: It’s worth noting here, that if you simply want to change the Blogroll title, then login into your Admin > Links > Link Categories and edit accordingly.
Always make a backup of any files that you alter.
Remove Blogroll Title from WordPress
Open bookmark-template.php, found in the wp-includes folder.
Around line 227 (see screen shot below), remove $catname
Remove the highlighted $catname from the above line in wp-includes