Url property has no such functionality out of the box unfortunately. Either extend it yourself = difficult because dojo is not a funny framework.

or use

LinkItemCollection as property instead. This has support both for text, title and targets on all links and supports multiple links. 

or 

add an extra property for text and control the rendering (dont use PropertyFor) and build your own a tag. 

or 

create a local block that does this and control rendering there to build your own a tag. 

I would go with LinkItemCollection normally :)

I just want to link to one internal page/external link,
1) Is LinkItemCollection the right choice for it?
2) How do I render it on the view? when I try to use as below, it is still rendering as normal url without any name to set for the link.

@Html.DisplayLinkCollection("<ul>{0}</ul>", "<li>{0}</li>", Model.Url)

@Html.PropertyFor()

For a single link it might not be the best match. But...a single item is a list of one link so :)

Otherwise go with local block that has both url and a string property for name. Takes a bit more code though...

I have created two properties

public virtual Url ButtonLink { get; set; }
public virtual string ButtonLinkName { get; set; }

In the view, I have rendered as
@Html.DisplayLink(Model.ButtonLink, Model.ButtonLinkName, true)

where DisplayLink is:

public static IHtmlString DisplayLink(this HtmlHelper html, Url url, string text = null, bool allowNoText = true)
{
return html.DisplayLink(url.Resolve(), text, allowNoText);
}

and Resolve function is:

public static string Resolve(this EPiServer.Url url)
{
return url.IsNullOrEmpty() ? null : ServiceLocator.Current.GetInstance<UrlHelper>().ContentUrl(url);
}

With the above code,
1) when the external link is entered and no name is given, it is displaying the complete url

2) When the external link is entered and name is given, it is displaying the Name as url and is redirecting to
the url given

3) when internal link is selected and name is given, it is displaying the name and is redirecting to the right page when clicked on it

4) When internal link is selected and no name is given, it is displaying the friendly url (
when home page is selected as the url, in the front end it's displaying as '/', if it's some other page it is displaying as '/page1/page2').
When clicked on friendly url, it is redirecting to the right page.

In the scenario 4, I want the page name to be displayed rather than friendly url. In the example above, Home needs to be displayed as opposed to '/',
in place of '/page1/page2', page2 should be displayed. And it should redirect to the right page when clicked on it. Scenarios 1 to 3 should not
get affected.

1. Use UrlResolver to get the content from url. Use the Route method on that class...

2. Get the page name from the content item.

3. If ButtonLinkName above is empty, use the above...