Instead of using the MM username the username on GitHub should be used. The user whose message gets links, might not be connected to GitHub. In this case fall to back the MM username.

I am interested in resolving this issue.
Does it mean that whenever an issue is created (or a comment is made) on GitHub, the user/channel getting the notification on MM should get the GitHub username (of the person who commented on/opened the issue) and not the MM username?
I have a confusion as the image shown here is that of a GitHub comment (and not of MM channel message)
Hi @abdulsmapara,
The ticket is about the the "Attach to issue" functionality, which you can find when clicking on the dot menu of a post. Is the ticket now more clear?

Ok! So it meant the "Attach to Issue" functionality of MM, thanks @hanzei for the clarification
So, is my understanding (as described below) for the ticket now clear ?
If a user X attaches a message from another user Y to a GitHub issue, X & Y's GitHub username should be used on the comment on GitHub and in case Y is not connected to GitHub on MM, Y's MM username is to be used.
Exactly @abdulsmapara