CI4 CMS

I am not sure you can copyright the use of the two letters CI. And CI is not the name of the framework anyway, it is just a shorthand for CodeIgniter. You could NOT call it CodeIgniter CMS I am guessing.

Crime and Investigation TV use CI as their name.
CI.com is city investments.
CI is Cigars International,
CI is Consolidated Independent, a music technology company
and that is just first few results of Google.

So I would say you do not need permission to call your system CI CMS. For instance you could say the CI stands for Creative Interface CMS, or Crystal Infusion CMS :-)

However, since you are using CodeIgniter as the framework of choice, you may want to make it clear that you are not endorsed or part of the CI framework, just to be clear and up front.

But CI CMS is an awful name anyway. Surely you can be a bit more creative with it :-)

I don't want to call it CI CMS Again someone was assuming I would call it that... maybe because of the topic or something... Anyways the name is the least of my concerns right now