Bath-born Kilgour, who joined the club initially when he was seven, has been named captain since returning for a second spell, with Southwood vice-captain.
After losing their first two games of the campaign back in League Two after relegation in May, Rovers have gone on to win their past three league outings against Cambridge, Grimsby and Newport.
“We’ve created a leadership group now and that’s six players in the changing room that represent the players, and they are the experience, they are the leaders,” Martin said.
“They are not just the older ones but they are leaders in the way they go about themselves and carry themselves, the way they influence the changing room and training ground.”
Martin started in the role this summer having previously been a technical director at Stoke until February 2024.
He spent 16 years before that as a coach at Norwich and was also West Ham’s academy director.
With his first transfer window at Rovers now over, Martin said the club could have done more but he was satisfied the squad was in a “better place” than before.
“That’s something that keeps driving me to get me ready for the next window so I’m even more prepared, I’m even more focused so I can ensure every time the window shuts we want our squad to be in a better place,” Martin said.
“We’ve got a better place now than when we started the window, but come January I’ll be going again.”