That's a great specimen of a rose, whatever it is. If you dig it up and plan to replant it somewhere else, may I suggest the following procedure:
1. Thoroughly water it for three days before digging it up.
2. Let the soil dry out a bit on the fourth day.
3. On the fifth day, cut the rose back by 2/3rds of its height. The reason is that a transplanted rose's roots cannot sustain so many existing leaves after being dug up and going into "shock".
4. Use a sharpened flat spade, rather than a rounded shovel, to "chop" a circle around the root mass. You'll need a sharpened spade to cut through the roots. If you have a flat spade and a metal file, sharpen the end of the spade.
5. Then use a rounded shovel to get down under the root mass and try to "pop" the rose out of the ground without loosening all the soil around the roots. In other words, try to keep some soil intact with the root mass (easier said than done).
6. Hoist the rose out of the ground onto a plastic tarp, without puncturing yourself with thorny canes.
7. Drag the rose on the tarp to its new location.
8. Dig a VERY big hole for a rose this mature.
9. Slide the rose off the tarp into its new hole, and fill in with crumbled, loose, dry soil.
10. Keep well watered for the next few weeks while the plant adjusts to its new setting and gradually comes out of shock.