Probably 'Dr. Huey', which is commonly seen because it is used as rootstock by a percentage of American commercial producers. In my area it tends to replace many of the roses grafted onto it over time, with involved parties apparently often not understanding what is taking place. For instance I saw a white climbing rose yesterday where half the top consisted of shoots of 'Dr Huey' that had been allowed to grow up and become evenly mixed with the white kind. Click on the Photos tab in the upper part of the page below for a number of different images to scroll through and compare your plant with:

https://www.helpmefind.com/rose/l.php?l=2.1550

That's 'Dr. Huey', a variety used as a rootstock to graft other (better) things onto. It has some bad habits that make it less than desirable as a garden plant, but if you like it, keep it. It flowers only for a few weeks in late spring, and that means that it blooms on the previous year's wood, so if you cut it back this summer, you are limiting how much it flower next year. If you are going to keep it, let it grow as it wishes, and train/tie back the canes to make them more manageable.