Hokay,
(deep breath....

)
I'm afraid you're barking up the wrong tree looking at patents for protection. A utility patent, as the name implies, protects inventions that are "useful". Neither utility nor design patents are meant to protect logos.
If you're talking about protecting the name of the clothing line and the logo, rather than the functionality of the clothing (which might conceivably be patentable) or the look of the clothing itself (which might be subject to copyright, and maybe--but I doubt it--design patent), then you're talking about trademarks. Trademarks distinguish one company/individual's items from similar items offered by another company/individual. A trademark is the "brand" that lets consumers know every item marked with that image/name/package design comes from one and the same source. And trademark rights come about just by using the trademark appropriately. If you federally "register" the trademark (what people usually mean when they use "trademark" as a verb), then you get enhanced protection for your mark.
Note also that if you are selecting a name for your business and you want to have your business name also be your trademark, as most people do, you will need to check out whether the name is available for use as a *trademark* not just whether your state's secretary of state will let you have it for a business name--also known as a "trade name", hence the frequent confusion with trademark. Registering a business name does NOT give you the green light to use that business name as your trademark. There are different standards at work. The test for trademark infringement is whether there is a "likelihood of confusion" between your mark and the mark for someone else's goods or services. For business names (trade names), the state just wants to make sure you're not fraudulently holding yourself out as another company--focusing on the business as a business entity. This is a different standard, and not as hard a standard to meet, as that of avoiding trademark infringement. Trademark infringement by contrast focuses on whether consumers might mistake your goods or services for someone else's or think your goods or services are connected with or sponsored by the other trademark owner in some way. So a small difference in a name might make it OK to register that given name for a trade name, but not be enough to make it safe for use as a trademark.
Now, you say your main priority is to protect the proposed name. There is a mechanism to do that before actually using the mark.
This is to file an "intent to use" (ITU) application with the Trademark Office of the US PTO. Before paying the expense of applying you will want to search both registered trademarks and unregistered trademarks to see if your mark might cause a "likelihood of confusion" with a mark someone else is already using. (This determination is best made by a trademark attorney, since there are various considerations that come into play.) After you file your ITU application, if and when your mark is cleared by the PTO, then ONCE YOU'VE STARTED TO ACTUALLY USE the approved mark, the PTO will register it and you will get a "priority date" on your mark that goes back to when you filed your application--rather that the time you started using it. This gives you the "jump" on anyone who might try to register a potentially conflicting mark in the interim while your business is gearing up.
The US Patent and Trademark Office (PTO) has information on Trademark Basics at its website. Check out
http://www.uspto.gov/go/tac/doc/basic/There are also quite a few threads in the various IP forums here that address the distinctions among patent, copyright, and trademark and ways to help secure trademark rights. A couple of recent replies on this topic I posted are at
http://www.intelproplaw.com/ip_forum/index.php/topic,11868.0.html and
http://www.intelproplaw.com/ip_forum/index.php/topic,11751.msg54572.html#msg54572(I offer these simply because my own posts are easy for me to find.)
The trademark Forum homepage also has links to the PTO and other sources:
http://www.intelproplaw.com/Trademark/Good luck. I hope all this helps!