I feel your pain on both counts:
1 – app names that seem different in the app drawer than than they were in the playtore
2 – difficulty keeping track of 300 apps and finding that latest one that I downloaded.
I have developed my own system to cope with #2 on Nova Prime Launcher
Create folders using Nova Settings / Drawer / Groups / Folder / “+”
...and remember to UNCHECK “Keep apps in main app tab”.
Put all your apps into category folders, then the number of apps left in app drawer (not in folder) gets smaller (only the ones not in folders show in the app drawer main list).. I also have a folder called “hide” for apps that I don’t really need in a dedicated folder (I have dedicated homescreen icon for example) so I can keep the number in the main app list really low...down around two or three. It's very easy to find your newly installed programs there among those two or three programs. This helps with #2. When I install a new program, I tend to leave it there (not in any folder, only showing in app drawer main list) for a few days until I'm satisfied I'm going to keep it, and THEN drag it into folder.
By the way, folders created in app drawer can be placed onto homescreen/desktop and act just like any other folder on your homescreen. And you can add to them afterwards by dragging icons in on the homescreen (and the effects show up in app drawer… that app disappears from the main app list). But you don't have to put all app drawer folders onto the homescreen - example the folder that I called "hide" is something I don't need to access to I don't put it on the homescreen.
Going to the effort to categorize each app makes it easier to find them when you need then of course, but also helps to keep track of what apps you have that are overlapping, so you can decide what to get rid of if you need to make more space.
If you should ever want to look at a list of all apps (the old fashioned way), you can’t do it in the app drawer, but there are other options to view the c0k-petemlist of all apps
1 - if you long-press to add app to homescreen you are presented with the old-fashioned list of all 300 apps.
2- use another app drawer,....I use my touchwiz launcher when I want to view the complete list.