If I find an Open Source project I like, but I rewrite the entire thing because it's poorly written. I don't mean the question where you rewrite it slightly different, so I can say it's mine or anything like that. I've seen those questions and answers. This is actually the opposite.
Example (only an example),
I take a project. I rewrite it entirely in an MVC framework. The original project had nothing even close to it. In fact, I change everything except I keep a database table. I take no code whatsoever, except a line or two that require me to say my work is a derivation of the original. Thus, I have to license it as such.
Can I say it is a fork or project X?
I ask because this is kind of the reverse of all the questions I have read. This question wants to know if you can keep calling yourself a fork. If you do this, isn't this just a way to make your new project popular or to direct traffic, "Open Source SEO." I don't mean you changed one line, so you can say you're a different project. I mean a whole rewrite, but you keep just enough so you are required to say you derived your work from X (just assume for the purpose of the question, the resulting project actually is better than the original). In short, a marketing technique.
Edit: Is this unethical?
Edit: I did find this, How to avoid being forked into oblivion by a more powerful contributor?