Personally, I believe that the most important things about a blog are the name, the design, and the content. In that order! A name draws you to look, and then if the design is visually attractive you tend to look around. If you have stuck around long enough to read the content, and you like it, then that is what keeps you coming back! So you want to come up with a good name!
But where do you begin right?
My response to this is to just sit down and write down words that you think describe you! If you have a nickname that is sentimental, or unique to you, then please use it!
My next bit of advice is to try to make it a name that you will not grow out of! I have gone through three different blog names to finally learn this! For example, before my blog was SimplyTiki it was The Momma Bear Diaries. While there was a sentimental reason behind the name, it was a name that was kind of limiting in terms of content. Yes, I will always be Momma Bear, but I reached a point where I wanted to post more than just "mom blog" posts. I outgrew my blog name. So try not to give your blog a name that just describes one form of content! You can detail the type of blog your doing in the tagline. It doesn't really have to be in the title.
My last bit of advice is just to have fun with it! While your thinking of a name that works for you, and is not limiting, have fun with it! Write a ton of ideas down and see if one sticks out to you!
So now you hopefully have a name for your site! Your next step is to create your free blogger account using that name and then go about purchasing your domain. There are so many different options to purchase your do,aim from. You can purchase through your blog or through the thousands of hosts out there. GoDaddy is my go to for domains. It's so easy to purchase and then you can call them and have them help you point your domain to your blog.
At this point you have successfully named your blog! Now you need to start thinking of design!