I saw a cool post on Diamond Jesters. Apparently it was originally from a blog called Shlabotnik Report. I see Night Owl has done this too. Best player who played for your team for the ten most common American surnames. (Plus Ramirez which started the original blog post.)
Here are my picks for the Yankees. It's been unclear whether you are supposed to base on the player's overall career or just what they did for your team. I tried to do a mixture.
1. Smith
There have been nine Yankees named Smith. Mediocre infielder Charley Smith played 181 games for them in the late 60s, by far the most of any of these. So I'll go with Hall-of-Famer Lee Smith, whom the Yankees brought in to shore up their bullpen toward the end of their surprise division run in 1993. He pitched eight scoreless innings in eight games, with three saves, but the Yankees didn't have quite enough to overtake Toronto.
2. Johnson
The Yankees have had double the players with the #2 name than they did the #1, with 18 Johnsons. Hall-of-Famer Randy Johnson did not acquit himself well during his Yankees tenure. Cliff Johnson was a key bench piece for two WS teams but got into a bad brawl with Goose Gossage. Instead I'll go with Billy "Bull" Johnson, a regular on four WS winning teams in the late 1940s and early 1950s.
3. Williams
Of the nine Williams men who played for the Yankees, this one is a no-brainer. One of the best switch-hitters and clutch-hitters in baseball history, Bernie Williams belongs in the Hall of Fame.
4. Brown
The Yankees have had seven Browns including two named Bobby. Dr. Bobby Brown was a teammate of Bull Johnson in the late 1940s and early 1950s, a key member of four WS champions.
5. Jones
The Yankees have had eight players named Jones. Andruw is probably the most famous but his Yankee tenure was not very good. Instead I'll go with Sad Sam Jones, who won 21 games, including a no-hitter, for the first Yankee championship team in 1923.
6. Garcia
The five Garcias who played for the Yankees make for some interesting choices. Damaso probably had the best career, but hit .228 in 29 games for the Yanks before they traded him to Toronto where he blossomed. Karim had a steady but unspectacular career, but did hit .305 with the Yankees in 2003. In the end I went with Freddy, who went 156-108 including 19-14 in two seasons in the Bronx.
7. Miller
Only five Millers and a pretty easy call to go with Andrew Miller, a dominant set-up man in his two Yankee seasons.
8. Davis
Eight players named Davis suited up for the Yankees. It's a tough call, but Ron was one of the first star set-up men, giving him a slight edge over Chili's two rings in two years in '98 and '99.
9. Rodriguez
Nine Rodriguez Yankees, with Alex the runaway winner here, beating out the brief Yankee tenure of the only HOFer in the group, Ivan.
10. Martinez
Only two for the Yankees, and while Tippy was decent, he can't hold a candle to Tino.
Bonus. Ramirez
Only three players named Ramirez played for the Yankees, and only Edwar, who won a ring with the 2009 Yankees, had more than a brief Yankee stint.
(I have all of these cards, but was too lazy to dig them out for this post, so I used TCDB scans.)