First, think very carefully about deleting your blog. I say this because once you delete a blog from WordPress it will be gone forever. WordPress does not recycle usernames (blogs or accounts).
You cannot foresee the future so your best option is to set your wp blog to private. Things happen and you may change your mind and want to return to WordPress with that username you liked so much at one point. Setting it to "Private" leaves you that option, does not cost you any money, and why burn a bridge if it's not necessary.
Here is how to set your site to PRIVATE:
select this option: I would like my site to be private, visible only to users I choose
As a volunteer here, I have no stake in your choice so here you go: You can delete that blog.
Here is the support article about how to do that:
As for mapping your blogger name to the domain you purchased, you need to contact support at Blogger for help with pointing your domain to a Blogger site.
This forum is (for the most part)is a peer-to-peer support forum. We answer questions about WordPress.com only.