Countif using specific criteria

I am using the CountIF formula to count how many times a name appears across several sheets (all within the same workbook). But I need to separate each name into two different categories. So, every time a name falls under Category 1, the name is typed regularly and CountIF adds it to the total.

If the name falls under category 2, I differentiate it by adding a * in front of their name. This makes sure that names with a * in front of it, are not added into the category 1 total.

Now though, if I use CountIF to try to total the names with a * in front of it, it just totals ALL of the times that their name appears even if it doesn't have an * . Is there a smarter way to separate the two categories?

For reference-- this is on an excel calendar I created so sometimes a name falls under a category 1 and a category 2 within the same sheet, so making a separate sheet and totaling it that way is not an option.