do search engines love wordpress domain name issue

I use wordpress.com for a blog.

I want to use www.ads-software.com for a squeeze/sales page with a blog format because I am told that search engines love blogs. So does the word ‘wordpress’ need to appear in the url? Would a self-hosted blog using wordpress architecture have an advantage over run-of-the-mill ‘blog’ templates that are essentially just web page designs?

I have web hosting organised. What would by my url in this case? Would it be https://www.mydomain/wordpress. (org) (com) or would wordpress not appear in the url domain name? Or something else?