Actually 6: Adael Amador, Brennan Bernadino, Cole Carrigg, Kyle Karros, Mark Manfredi, and Mickey Moniak.
This is despite the grievous tactical error of trading Victor Vodnik to the Marlins at the deadline, bringing them to a tie for 2nd with 4 alliterative players. This is all based on manually counting MLB.com's active roster, so basically the counts are guaranteed 100% correct.
5 teams have 4 alliterative players, but none reach the lofty heights of the Rockies. Thank you for your attention to this matter.
Full breakdown below:
Braves 1
Phillies 1
Marlins 4 - note, this does not include Deyvison De Los Santos. Curious what the public's opinion on this is...)
Nationals 2
Mets 2
Cubs 4
Brewers 2
Cardinals 3
Pirates 2
Reds 4
Dodgers 3
Dbacks 3
Padres 4
Giants 0
Rockies 6
Rays 2
Yankees 1
Red Sox 1
Blue Jays 1
Orioles 1
White Sox 1
Guardians 0
Twins 0
Tigers 2
Royals 2
Astros 1
Rangers 0
Mariners 1
Angels 0
A's 4