Use the 'create historical league' option. In the league structure, change the names of the teams/nicknames or randomize it.
The Lahman database doesn't have any information on minor leagues so you won't be able to create the same minor league structure.
If you want to maintain the minor league structures, the theortically way to do it is to..
1. Create a historical league starting in 2006.
2. Export the roster set
3. Create a standard league with the inaugrual draft.
Here's where it gets tricky. I don't know how to do #4
4. Delete all the players in the standard league
5. Import the roster set
6. Run your draft.
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