Question

I heard something about Google has some priority for .us or .name domain names for assigning page rank to them.
For example, with the same situation for both a .at and .us domain name, the .us domain name will have higher page rank that .at.

I want to know is that correct or not?

Answer 1

No. Matt Cutts, head of the Google Web Spam team, explained a lot about TLDs in this video:
http://domainate.wordpress.com/2011/11/10/matt-cutts-discusses-new-top-level-domains-and-google/

There is no bias against TLDs, or as the article quotes:

1. Google will not have predisposed bias against new TLDs

Matt makes it clear multiple times that Google strives to return good
relevant results regardless of the TLD of the domain. He even made a
point to indicate that Google has no bias against the recently
released .XXX.

Although the writer does add:

What I think: Matt has said before they do not take TLD into account,
but many studies have shown that to not be true. The truth is, they
may not directly bias against TLDs, but factors like domain and site
age are factored into their algorithm. New TLDs have disadvantages in
both compared to established sites/domains in other extensions.

Some people later thought that Google would artifically favor new TLDs to make up for that, but here’s more on that:
http://domainate.wordpress.com/2012/03/15/matt-cutts-confirms-new-tlds-will-not-get-seo-preference/

Google has a lot of experience in returning relevant web pages,
regardless of the top-level domain (TLD). Google will attempt to rank
new TLDs appropriately, but I don’t expect a new TLD to get any kind
of initial preference over .com, and I wouldn’t bet on that happening
in the long-term either.