There aren't any exciting names who absolutely need to be added to the 40-man roster in order to be protected from next month's Rule 5 Draft. Nor are the bubble candidates much to wring our hands over, as they're maybe bullpen arms in the future. But let's go through them and you can decide:
RHP Brandon Brennan is perhaps the closest thing to a "need to add", in my opinion. The 2012 4th rounder has been snakebitten by injuries. He had Tommy John surgery in 2013 and then he missed the first couple months of 2015 with a neck injury. The 24-year-old has only made 55 appearances (48 starts). While he hasn't appeared above High-A, the White Sox assigned him to the Arizona Fall League as their starting pitcher contribution in order to get him more innings. He's got a decent four seamer that sits around 93 MPH and also throws a slider and changeup. His control isn't good - he's got a 9.6% walk rate at High-A - and he doesn't strikeout enough batters to make that work. He's probably a bullpen arm long-term. I think he's a guy that could still develop into something interesting, and even with his limited experience I could see a team taking a flyer on him, so I'd be inclined to add him.
RHP Myles Jaye is another guy who is on that bubble. Since acquiring him from the Blue Jays, the White Sox have continued to develop the soon-to-be 24-year-old as a starter. His repertoire isn't remarkable. The velocity on his fastball is a tick or two below average at around 91-92 MPH. His slider and changeup are okay. In his second go-around with Birmingham in 2015, Jaye at least did what you're supposed to do and improved. I've thought for awhile that he should become a reliever because I think he's well-suited for it. I think a team might draft him so I'd be inclined to add him, too.
RHP J.B. Wendelken is another guy with an unremarkable repertoire. He's got a couple fastballs. His four seamer tops out at 93-94 MPH, which is nothing interesting for a reliever. He throws some other pitches. He's got AAA experience and has gotten decent to good results in Birmingham and Charlotte. He's still relatively young, as 2016 will be his age 23 season. He has a decent chance to survive in a major league bullpen next season so I'd add him, too.
RHP Peter Tago has a big arm but little idea where it's going. In the AFL, he's walking a lot of batters. More than he's struck out. I think it's safe to leave him off.
LHP Onelki Garcia was outrighted off the 40-man prior to opening day, so that should tell you how much teams would be interested in drafting him. The Cuban's 2015 season was basically like all his minor league seasons (and brief major league time with the Dodgers): struck out a lot of guys but walked a whole lot of guys. Still, he's a lefty with a power arm so I guess maybe some team might want him. I won't care if he gets drafted.
1B Keon Barnum. Um, no.
The 40-man sits at 34 players right now so there's plenty of room to add. Players have to be added today to be protected. It costs $50K to draft a player. To keep him, essentially he has to be on the 25 man roster for all of 2016. Otherwise, he's offered back to his original team for $25K. The draft takes place on December 10, the last day of the Winter Meetings.