Is it possible to get the property(get; set; ) say Name from code behind(aspx.cs) file into jquery?
Yep. If your script is inline in the aspx page, simply use the ASP tags to get it into the script.
public function myJSFunction()
{
var x = '<%= Name %>';
...
}
If your script isn't inline, i.e. it's coming from a separate javascript file, you have a couple of options.
You can add the variables that you need into the page using the technique above, and then your external javacript can reference it.
You can make the external javascript file a web resource by changing it's content type to "Embedded Resource" in the properties window, and then using the following:
[assembly: WebResource("myJS.js", "text/javascript", PerformSubstitution=true)]
The use of the "PerformSubstitution" flag on a WebResourceAttribute will make it so that the file is run through the asp parser before it is rendered, and it will replace any ASP tags it find in the file. Web resources have some drawbacks though so you should read up on them before deciding to use them.