Milihime Promotion Format
There are 4 stages of promotion for a girl (many with only 2). The most notable one is the 昇 promotion when the girl gets a new vehicle.
昇 means rise (probably rise in rank) and can be pronounced as both 'noboru' or 'shou'. Noboru seems long and tedious to say, so we'll go for Shou. Now, this applies to 昇, not II.
So, it'll go like this
Bronikowsky Shou Kai
Update: Kai is an official term for 'II'. So, follow as per above.