Edit, Tl;DR Zamasu from Future Trunks Timeline is likely Zamasu from the regular timeline, who learned about Goku from Shin, and then traveled into Future Trunks timeline because Shin (and therefor Berus) was dead. This then caused Future trunks to travel back in time in the first place.
I do not know how to add pictures, or I would, but the full chain (if the manga will indeed show the same main events as the anime) was likely completed in the most recent chapter of the Manga.
There is the anime's version to consider though, so I will note both, starting with the anime.
In the Anime, It is basically due to a time loop. Future trunks goes to the past, bringing Black with him, who then fights Goku. Goku then learns about and visits/spars with Zamasu. It is here Zamasu learns about Goku in the anime.
Zamasu then went and learned about Goku from the guy who knows everything, as well as the super dragonballs. He then uses them to wish for either immortality, or an ally like Goku. He then likely used the ring of time to skip ahead and gather them again, quickly wishing for the other wish. He then finds the timeline where Berus is no more, and goes there so that there is no one to stop him from killing Humanity.
The Manga version of the story is not as detailed, But if we are to assume that the main plot points of the manga will be identical to the anime, then we have a better version of the loop thanks to the most recent chapter.
In chapter 16, page 36, Zamasu is talking with Our own Kaioshin, Shin, and Kibito, after sparing with Kibito, about how they took out Majin Buu. Shin brings up the fact that he only helped Goku and the other Z Warriors do so. Zamasu at this time learns of goku and how powerful he is. This is all we know in the Manga so far, but we can probably assume the details will play out like in the anime, so he will likely soon go and try to learn about goku from the guy who knows everything soon.
There are 2 things that make the Manga version a more "stable" version, first in that Zamasu learned about Goku from Shin, and second, that Shin was Probably visiting Zamasu without any interference from Future Trunks, since he appeared at about the same time they were visiting Zamasu. If he had not shown up, Zamasu would have found out about the super dragonballs and made his wishes without anyone knowing about him.