im wondering how i can get a new country with a new name and everything. but is it possible for me to even do that?

I'm assuming you mean something like Spain's civil war, where you will have Carlist Spain, Republican Spain, etc.? 

If so, this is usually done with cosmetic tags. You will have cosmetic tags for each side of the civil war you wish to have a new name/flag/colour/etc. and assign the cosmetic tag to the breakaway nation.

This way, when trying to target your country or the civil war breakaway nation(s) you are able to use "original_tag = TAG" to target them (for things like does the country exist, who to send events to, etc.)

However, if you want both nations to be able to exist forever, for example, North and South Korea. Then you will need to create your breakaway nation as another country, that gains cores on its rightful land when a focus/event/etc. fires which starts its war. And then possibly give the original country a cosmetic tag so that it has a new name; if you feel it fits; for example, if Scotland, Northern Ireland, and Wales leave the UK then the nation gets renamed England.