There will be no reputation changes after finishing the DLC.
Ending messages and perk descriptions have also been edited to reflect this.
Requirements
DLC requirements
DLC name
Lonesome Road
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I'm not going to get too much into this, but there is a good argument that regardless of what you do in The Divide, there's no one that can really link you and your actions together.
Even if you spare Ulyssees it's unlikely that he'll blab to everyone that you're the one that launched the nuke/stopped it from launching.
Likewise, you shouldn't get immediate reputation changes within the factions and the most that wastelanders can make sense of what happened is only speculate your role in it. The ending messages after the quest will briefly reference this.