On the screenshot we don't see the top of the history log.

Without scrolling up. Are you able to tell me which branch the red line is associated to ?

This is a good example that shows why users wants a way to quickly/easily know which line is associted to which branch.

According to the commit messages I guess the green line is the branch "(origin/)smartsvn" but not the red one, it would be easier to have a way to get this infos when moving the mouse pointer over the green line or the branch name in the branches tab.

Maybe if the user selects (not check) a branch name in the Branches tab you could highlight the associated path in the commit tab.

The log shows if a commit was pushed when we checked out v4.93.xx or creatique_1132 so can retrieve more information that you say.

Yes it is...but after a merge...

If I push new commits to branch creatique_1132 the blue line will get extended next to the red line which represents branch v4.93.xx. as in the example below (other repo).

We just want to know which branch is represented by which line and not which branches is contained in which branches... We can already see it when lines move to another line.

The purpose of the Log window is to make the history human readable otherwise we can use a terminal window.

Or using a tooltip with the branch name as suggested Thomas Hansen.

Maybe adding colored rectangle next to branches names would help in some cases...