If you bought it locally in a pot, then it is grafted. Otherwise, the only way to tell now would be to dig down and find the graft union (big knot where the canes meet the rootstock).

If it didn't bloom last year, and you are getting really thin canes three feet away, I'm thinking your McCatrney is now Dr. Huey. Did you prune it last year? Dr. Huey is a once-blooming climber, and if you pruned it, you won't see any blooms, since it blooms on the previous year's growth.

I bought my rose over the internet five or six years ago as a bare root rose but I no longer remember the website! To clarify, my rose bloomed beautifully last year, here is a picture. It's the tiny plant that hasn't done anything, and I have left it entirely alone. I'm not going to prune it until I see what it is.
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Here are pictures of the base of my rose. Most of my strongest brand new canes have come from below what I thought was the bud union, and they are McCartney.
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Here's a picture of the little plant and its position relative to my McCartney rose.
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That is quite a distance for a runner to emerge. It won't hurt to carefully dig away soil on top of the new sprout to trace it to its origin. I suspect it came from below the bud union. As far away as it is from the McCartney rose, is it possible that another rose was in the spot where the new cane emerged? I had a once-blooming climber that kept emerging from the root until I was able to get all the root dug out. It took several years.

Gary

Wait until it blooms. It looks like a different rose.

I suspect it's the root stock. It appears to be very vigorous with long thin canes which is symptomatic of Dr Huey.