Two really important points that are covered within this thread - but not on page 1 - so someone who only looks at the (incredibly valuable!) first post might miss them. With these 2 tricks, in conjunction with the info in the first post, you can almost always identify EXACTLY who the player is, even those modern RPs with 10/10 K and BB ratings and A+/D- fielding (of which there are like a zillion in the database.)
1.) Click on the player and check his salary history. One of two things will happen.
(a) You will see how his salary changed during the 2015-2017 dynamic pricing history, including his "final" salary. This will usually pinpoint the exact player.
(b) You may see "no changes in salary" which immediately tells you that the player is from a season no further back than 2017. This can help narrow down the set of possible players considerably.
2.) When you go into the GM center, you will see your entire roster, including AAA players, in alphabetical order. Your AAA guys will initially look like they are out of place - according to their AAA name. But the thing is that they are PROPERLY placed in alphabetical order according to their real name. So you can usually pinpoint what letter(s) their last name could start with, within a very small range.
Using these two tricks - again, in conjunction with the info on page 1 - you can almost always identify the exact version of the player who have been given.