You would need a separate field to store the link text, apart from the link URL, and then when outputting the URL field construct your own link markup where the href attribute comes from the raw value of the URL field and the anchor text comes from the link text field.
When you say separate field, do you mean a completely separate custom field? I think that would probably be too complicated. Or is it possible to add a sub-field to an existing field, or make a new field type based on an existing one maybe? I don't mind getting my hands dirty, if it's possible to do it.
It's a pity an option for link text isn't in the URL field, as you end up with a lot of ugly URLs cluttering the page. And it's a basic part of adding links.
