Well, his relationship with Vegeta would be interesting. If Goku went back in time and showed Vegeta the SSJ God form too early, Vegeta might become more competitive or even jealous earlier. He might push himself even harder to catch up, which could lead to more intense rivalries and also more joint training sessions between them.
Goku's relationship with his friends like Krillin and Yamcha would also shift. If he changed the past and made the Earth a safer place earlier, they might not be as battle - hardened. Or, if he introduced new training techniques from the future, they could become stronger and their friendship could be based more on mutual growth in power rather than just the shared history of fighting common enemies.
With his family, if Goku time - travels and changes the past, his relationship with Chi - Chi could be different. For example, if he was able to prevent certain threats earlier, he might be around more for his family, and Chi - Chi might not be as strict or worried all the time. Also, his relationship with Gohan and Goten would change. He could train them in different ways depending on the knowledge he gained from time - traveling.