Supporters of other teams appear to have grown increasingly eager to push the belief the Ibrox outfit is a brand new entity over the last couple of weeks in particular.
That follows the failed move to take Rangers Football Club plc out of administration via a CVA and the consequent decision to liquidate it.
The reality is that while the old holding company - founded in 1899, 27 years after Rangers itself - is to be wound up, the club formed in 1872 remains.
With it stays its proud history, during which it has won a world record 54 league titles and 115 major honours in all.
As such, Wallace maintains that while there may have been major corporate changes off the park, that doesn't mean a new team will be playing football at Ibrox this season.
He told Blues News on RangersTV.tv: "I'm still wearing a Rangers badge on my chest when I go out to train.
"I'm still going to be going out on a Saturday at Ibrox and nothing has changed in that respect. It's still Rangers that I'm playing for.
"In that sense, they've absolutely not died and it's down to all the boys who are still here to put us back where we belong.
"There might be a tough season ahead for us but that's what you expect as a footballer. You come up against obstacles that you don't want to happen but you get on with it.
"You roll your sleeves up, you are professional and you get down to business. We might be down just now but we'll certainly not be there for long and we'll get back on track.
"This is a new chapter for us but that is all and it's business as usual as far as I'm concerned. It's our job as professionals to continue doing what we do."
Rangers will almost certainly be relegated from the SPL for next season and moves into the First Division and Third Division have both been mooted.
Wallace admits there is something very attractive about remaining at the club as it drops down and trying to help it become as strong as it was before again.
As much as anything, he puts the backing from Gers supporters down as a major reason to stay behind and try to deliver success once more for them.
He added: "This is a rebuilding process and I'm saying that I'm happy to be part of it, as are the guys through in the dressing room now.
"I think that's going to be the most important thing for us. We need to roll our sleeves up and soldier on. That's exactly what we need to do.
"We need to stay tight as a unit and as a family and just move on as we look to get us back to where we should be.
"Last season when we went into administration, we almost had a run of four defeats in a row at Ibrox and I don't think that had ever happened before.
"Even so, we'd get to the final whistle of games and when the fans were still applauding us despite our results, it was massive. Their pride in us as a support was fantastic."