Usual rules: last names only are fine. You get the start date and the length of the streak as a clue. Unfortunately, the embed feature on Sporcle seems to be broken at this point. I've got an email in to support, but for the moment, you will have to click this link to take you over to Sporcle and play the game there. My sympathies are with you during this difficult time. Don't forget to come back and report your scores. :) I got 33 of the 39; if you get the majority, you're doing pretty respectably, I think.
Bonus. A couple of weeks ago, I ran a Saturday Sporcle in which the challenge was to name all the players who appeared for the Diamondbacks in 2013. Figured we should revisit the results and see who was remembered and who wasn't...
And here are the overall results, broken down by number of correct answers.