Is there a way to adjust desktop links or shortcuts so that the name do not get truncated?

By Truncated do you mean "This is a na..."?

If it is folder view you are using, right click on folder view > Folder View Settings > Display (on left column) and increase the "Number of lines" in Text Settings.

For an icon placed on the workspace directly, you might need to increase the icon size.

How does changing the number of lines expaneld the horizontal width for text to be displayed? I tried your suggestion, but it didn't work. It just makes the Folder View have a vertical scrollbar.