One style guide that addresses the question of website titles in some detail is The Chicago Manual of Style, sixteenth edition (2010). Here is most of the guideline it provides:
14.244 Titles for websites and blogs. Websites should be referred to in text and notes by specific title (if any), by the name of the sponsor or author, or by a descriptive phrase. Some sites refer to themselves by their domain name (the first part of a URL, following the double slash and ending in a domain-type indication such as .com, .edu, or .org); such monikers, which are not case sensitive, are often shortened and capitalized in a logical way (e.g., www.nytimes.com becomes NYTimes.com; www.google.com becomes Google). Titles of websites are generally set in roman without quotation marks and capitalized headline-style, but titles that are analogous to books or other types of publications may be styled accordingly. Titled sections or pages within a website should be placed in quotation marks. Specific titles of blog entries (analogous to articles in a periodical) should be in quotation marks. ...
The main advice in this guideline—which happens to coincide with the practice we followed at the tech magazines and websites where I've worked—is to use title case (initial caps) when possible, to use regular roman type (not italics) for the title, and to run the title without quotation marks. For pages within websites, the guideline recommends adding quotation marks to the page title. Thus, for example, Chicago would endorse referring to this website as simply English Language & Usage and to this page of the website as "Case of website names in written communication."
Many alternative schemes for handling website titles are imaginable, but Chicago's has the virtue of proceeding somewhat analogously to its handling of short-story collections and music albums (except without the italics for the main title).
Chicago doesn't take a rigid position on whether the .com suffix should be included in the website title. This reflects the reality that some entities (especially ones with a real-world presence as well as an Internet presence) favor including the .com suffix to make clear immediately that they are referring to their online incarnation. Others show no inclination to include the suffix. So if you follow the companies' preferences (which seems reasonable enough), you'll end up with inconsistent treatments from one website to another. To that I say, "So be it."
One problem that Chicago doesn't address is how to identify a website that is inconsistent in its treatment of its own name: BLAHBLAH.com in its logo, Blah Blah in one piece of running text, Blah-blah.com in another, Blahblah in a third, and www.blahblah.com in a fourth. This type of inconsistency is far more frequent than you might imagine; and in dealing with it, our online publications either went with the site's predominant treatment of its name (modified by our refusal to reproduce all-caps formatting) or with the one that we liked best. We also had a standing house rule to capitalize the first letter of the website's name (which is what Chicago's "headline-style" treatment tends toward as well).
Whatever style rules you adopt for dealing with website names, the one constant that I would urge you to observe is that you shouldn't treat the same website name differently in different places. Beyond that, you''ll inevitably be dealing with websites that take very different approaches to naming themselves, and enforcing uniformity on them is likely to produce undesirable results.