If you had a 100 mL of 2.00 M HCl and you added 100 mL to it what is the final volume and final concentration?

The volume would be 200ml, but would the concentration just stay the same?

No and no. First, the volume will be 200 mL ONLY IF the volumes are additive and they are not(but they will be so close you will call that being picky). If you assume they are additive then the final concn will be

2.00 M x (100 mL/200 mL) = ?

Just a note: If you add 50 mL ethyl alcohol and 50 mL water together the final volume will be about 95 mL. Some solutions are so close to being additive it doesn't matter too much; others are not closer at all. That is why when chemists make up solutions (for example the problem above) they will take 100 mL of the 2.00 M solution, place it in a 200 mL volumetric flask that has a mark at 200 mL. Then we add water to the flask TO THE MARK which means that the final volume is 200 mL. We don't know exactly how much water is added but we DO KNOW the final volume and that's what we want.