All the above is correct:
1.- Ships were sometimes identified using recognition books, but more often through the last distress signal or debris that has the ship name (There are lots of pictures showing U-Boat commanders carrying life preservers of ships sunk) and finally also by asking the survivors.
2.- That said, the main method of constructing firing solutions did not involve a certain identification -unlike what you are forced to do in SH3 if you want to have a usable mast heigth for the stadimeter- but instead a guesstimation of the ship's dimensions. Here's how it was done for merchants: Cargo bays were counted (They can be seen as spaces between loading cranes) and then a certain figure was applied for each type of ship: F.e. small ships 1000 GRT per cargo bay, Medium ships 1250 GRT per cargo bay, big ships 1500 GRT per cargo bay. That gave a quick figure for tonnage, and also for ship's length, because 99% of ships have a certain proportion or ratio between length/width/keel depth/tonnage that is considered by naval engineers as ideal for stability and hydrodinamics. Ship length then allowed quick estimates of ship speed, but the primary and preferred method of getting speed and course was to follow a parallel course for some time, not necessarily at 90º AOB, but simply paralell, looking for a constant bearing.
I could write a lot more about this, and I really should do it somewhen
because I'd like to share with everyone all the info I have been collecting for many years, but I lack the necessary time and have other priorities now.