The "clean price" of a bond has a technical meaning. It is the invoice price of a bond (which is what your formula refers to), less the accrued interest. (The invoice price is the total dollar amount you pay when you buy a bond.)
The invoice price of a bond is mapped to the yield using the formula you give. Yes, this is equivalent to an internal rate of return. (There may be small technical differences between a bond yield than an internal rate of return; bond yields have a slightly more complex quote convention. Your formula is only an approximation.) It is a "quoted price" if the price comes from some source of market pricing. Most price quotations refer to the clean price; you need to add accrued interest to get the invoice price.
This would not normally be called a theoretical price, it is just a straightforward application of a pricing formula.