It's just henchmen you can't get, you still have your two main dudes. There's no effect on companions at all. The character(s) who have it get way more hp to start and extra ability points & talent points to spend on leveling.
Just did a test on this, started a new game, picked lone wolf on both, and ran to the city. It does effect companions.
In the game there are the two main characters, Roderic and Scarlett. Each of those can have one companion.
There are two named companions in the game so far. Madora and Jahan. Similarly to games like Baldurs Gate and such, Madora and Jahan both have full backstories and side quests tied to them. There will be more named NPC companions like these patched in later.
In addition to those, you can hire henchmen in case you want different classes to accompany you other than what Madora and Jahan are. These however are the generic mercenaries without any stories tied to them.
However, if you pick the Lone wolf perk, it fills up the companion slot for the main character. So picking it on both will mean you can never (unless you can remove it somehow later) do any of the quest lines or story tied to Madora or Jahan, or any of the other named companions patched in later. When picking the lone wolf perk on both characters, when talking to Madora or Jahan, they just reply with something like "You seem to be full up on companions at the moment".
So for me, I am not touching that lone wolf perk as it will remove story lines / quests, not just the ability to hire nameless henchmen.
EDIT: Also, this might be something patched in the final version, but as of now, when you discover a waypoint, you get the explore exp for it, but it doesn't activate unless you click on it. In the first city, you can end up being transported to a portal area, that will be impossible to get out of unless you have activated a portal before you get there. Have to reload an old save if you don't do it. So, when you get to a new waypoint portal, take the two seconds to actually run up to it and click it.