Hyperlinks in Word have multiple parts, just as in HTML
This is probably most easily seen looking at the Insert Hyperlink dialog. You can view this dialog using Ctrl+K or Insert > Links > Hyperlink. You do not need this to paste a hyperlink but it is useful to see.

That inserts the hyperlink Global Templates in Microsoft Word. The URL or address is http://www.addbalance.com/usersguide/templates.htm#Global. It is directing to a bookmark Global in the page. It looks like this when entered:

Hyperlinks are fields, most of which you can see by toggling field codes Alt + F9 in Windows. This one looks like this:

Notice that the Display Text is not shown in the field as displayed even though it is clearly there. This is a defect in this field display.
If there is a screentip it will be shown.



You can get back to the dialog which would show the display text by editing the Hyperlink.
Back to your question
When you paste into word, what you need to do depends on what it is you paste.
- If it is a live hyperlink with display text and possibly a bookmark, you would want to use the Merge Formatting option as shown in an earlier answer.
- If it is a bare text URL you would want to simply paste as text, select it and use the
Ctrl+K shortcut to add your display text.
- If it is the name or display text, you would again simply paste as text, select it and use the
Ctrl+K shortcut to add your URL or Address.