Like if i took three of the 6 protons from carbon, is it still carbon?
No, because the number of protons determines the identity of each element and is unique to each element. If you look in your periodic table, the atomic number of each element is different. The atomic number represents the number of protons each element has. For example, hydrogen has atomic number 1 since it has 1 proton, similarly helium has atomic number 2 so it has 2 protons. Now back to your question, if you took three protons from carbon (originally it has 6), you will now only have 3 protons, and the element with atomic number 3 in the periodic table is lithium so you would have lithium not carbon.
The addition or removal of neutrons may change the property of an element, making it radioactive for example. But most of the time, chemists are concerned with the number of electrons each element have. A simple example would be sodium metal. In its atomic form, it has 11 electrons and the metal is usually stored in oil because it reacts (sometimes violently) with any water present in the atmosphere. But once you remove an electron from a sodium atom, you get what is known as an ion (an atom which is charged) and the sodium ion is very stable and does not react at all with water. In fact, table salt is made of sodium chloride which contains sodium in its ionic form and it is perfectly fine to eat
I hope I have answered your question