Every link you enter into your Blogroll must be assigned to a Category, even just blogroll and, the Links widget must be placed in your sidebar in order for the links that you entered into your Blogroll to display.
The Links widget cannot be configured. All wordpress.com blogs have only one Blogroll located in the Admin area where you enter all links and assign each link to one or more Categories.
The links you enter into your Blogroll are displayed only after the Links widget is placed in your sidebar. Also note that there must be at least one link assigned to a Category before it will appear in your sidebar.
Likewise, the Category widget must be placed in the sidebar for posts to display. And just like links when it comes to posts there must be at least one published post in a Category before the Category will be displayed in your sidebar.
Once your Links widget and Categories widget are positioned in your sidebar, the manner in which the links you entered into your Blogroll will be displayed is alphabetically in accord with the Categories you created and assigned to those links when you entered them into your Blogroll.
Therefore as you will have multiple Categories it may look like you have multiple Blogrolls when you view your links in your sidebar. But in truth, you only have only one Blogroll, which is displays links as separate alphabetically ordered groups, in accord with the Categories that you assigned to those links when you entered them into your Blogroll.
The Blix theme is an exception. It's coded to display all links alphabetically without any category sub-divisions.