Yes, Rosa banksiae (aka Banksia Rose, Lady Banks Rose.) Could have white, yellow or cream flowers. As tough as old boots, practically unkillable.

Can be pruned back to the ground and will come back strong. BUT, it flowers on last year's growth, so hard pruning means no flowers for a year.

It looks like you have a Hesperaloe under it.

It does look like lady banks and from your description of it sounds like it too which is why we got rid of ours! Here in Las Vegas it’s bloom period is so short and it wants to grow so big it just wasn’t worth keeping for us.

If you don’t mind the brief bloom period or the work maintaining it and decide to keep it I hope you will rescue that hesperaloe from its clutches. It’s such a good plant here you would probably get more bloom from it if it wasn’t swallowed up by that thug of a lady banks!

OH! Hesperaloe! That's what I was told was a desert yucca! So, we actually have 2 of these lady banks. And I hacked the heck out of one because I was so annoyed that it was completely covering the other plant under it (the hesperaloe). And now that I know how tough it is, I might just go crazy on the other and save the plants under that one as well. Because, as mojavemaria says, they are just taking over and don't bloom for very long. No idea if I'll keep one or both; one of our dogs LOVES running under it when it's in bloom - he's a mastiff. It's really weird.