Git avoiding "merge branch master"

We have a case that is similar. Though we use a central master repo, we often have individual developers generating the Merge branch 'Master' message. Our solution was to have developers do git pull --rebase whenever pulling from the remote master repo.

I think you are looking for git rebase.

Each of the merges recorded in your history was required from the "preserve true history" point of view. Your branches diverged at this point, and were subsequently merged (note how both branches have commits unique to them, so fast-forwarding isn't possible.

If you rebase, the current tip (including the changes from your colleague) becomes the new branch point, and unless they push in between, your changes can then be applied by a fast-forward, giving the impression of linear development (but with non-monotonic timestamps).