Carsen Edwards
Marcus Smurt
Semi Ojeleye
Robert Williams
French Big Man
?
The whole idea of a "second unit" is an abstraction. It's a reality for coaches, because 5-on-5 play is an important part of practice. But the reality in a game is that there's a rotation, and this abstract "second unit" is virtually never on the floor together.
So I'm going to answer this question by ranking the players 1-10. This is not a ranking of how "good" these players are (those kinds of things wind up being a long dark trip down the rabbit hole). It also doesn't mean that I'm predicting a ten-man rotation - I'm not. And this is pretty close to a ranking of how many minutes each player will get, though it's likely that, as in recent seasons, the 6th man could have more minutes than one of the starters (I chose Smart for that role, as he's done in the past, but there are good arguments for Brown or Hayward...). In any case 1-5 are the starters, and 6-10 are the five most likely to get minutes after 1-5.
Clear as mud? Here we go.
1 Kemba Walker - like Kyrie, and like Isaiah Thomas before him, his ability to move the ball and create good shots will mean that he leads the team in minutes. That doesn't make him the "best" player - or mean that he'll score the most points. In fact it might just be better if he didn't.
2 Jayson Tatum - getting him plenty of good shots is a priority. The work he did in Summer 2018 to build iso skills was valuable but let's dial it back and get him better integrated.
3 Jaylen Brown - who comes off the bench, of Brown, Smart, or Hayward? I can see arguments for any of them, and they've all done it in the last couple of seasons. The coaching staff have praised Jaylen for accepting his role off the bench, for being a "rocket" when he comes off the bench, and for his lack of ego in accepting the role.
4 Gordon Hayward - as a coach recently said, “Look, the kids are the key. We need Jayson and Jaylen to be our dogs. They need to be badasses. We know Kemba is gonna be great. Our bigs are all skilled in different ways. But, Gordon is going to be the dude who unlocks everything. He’s so skilled in all facets of the game." Of Brown, Smart, and Hayward, I'm predicting that Hayward is least likely to come off the bench.
5 Enes Kanter - Opposing coaches are going to automatically want to put the Celtics in 1-5 pick and rolls. We'll see how this goes... Boston has been one of the top teams in the Brad Stevens era for defending the 3-pt line, so maybe Kanter dropping back all the time will work... On the other hand Boston's mid-range game just became more productive because of all the pressure that Enes puts on the offensive glass.
6 Marcus Smart - I'm thinking that we'll see more of the style that Brad developed in the IT era, with Smart coming off the bench and Kemba playing off the ball. Could be that it would work better to have Smart starting to keep the team defense organized, now that Horford is gone, bringing Hayward or Brown off the bench.
7 Daniel Theis - first big off the bench. I see people proposing Poirier in this role, and I have to admit that I just don't know enough about him. But Theis gives you rim-protection and outside shooting, and he improved substantially from year 1 to year 2 (I've seen people claim the contrary, but that's frankly mystifying; usually when such claims are made only a few things are being compared, like FG% or something; but Theis shot .388 from 3 last year - he's beginning to stake a claim to unicorn status).
8 Carsen Edwards - yes, he's only a rookie, and he'll take some lumps. But he's perfectly suited to take over the Terry Rozier role of raising the tempo off the bench, shooting with range, and creating shots off the dribble; and with Terry gone, a big opportunity for him is available, and he appears to be the only one on the roster who can do it. I'd throw him into the fire and see if he can swim.
9 Semi Ojeleye - like Theis, he showed a substantial improvement from year one to year two. In his case, the big growth areas were team and individual defense, and attacking closeouts with the dribble, and finishing at the rim. He got the hang of when to help (too eager to help one pass away in his rookie season, for example), and was getting up under his man and in his airspace (he was already terrific at staying in front). He's got a repertoire around the basket, including moves that get him to the other side of the rim and using it as protection, getting the ball up high at a difficult angle; like Smart, his effectiveness at the rim took a big leap forward.
10 Robert Williams III - the team thinks that he can be special, even as they temper expectations. I predict that he won't be in the rotation to start the season, but he'll get there by the All-Star break.