I grow 'Lyda Rose' and it appears to be the same as your rose. 'Lyda Rose' is very healthy, shade tolerant and quite fragrant and I love its' pretty foliage nearly as much as its flowers. Photos of it can be seen at helpmefind.com/roses

Luxrosa

Looks like some species rose to me. (Although I doubt the species is Rosa multiflora. That's not impossible, but I doubt it.)

Any chance it is some version of Rugosa?

See the link below for Lyda Rose as Luxrosa suggested.

White, near white or white blend Shrub. Registration name: LETlyda.
Origin: Bred by Kleine Lettunich (1994) United States.
Class: Shrub.
Bloom: White, pink edges, pink reverse, yellow stamens. Strong fragrance. 5 petals. Average diameter 2.5". Single (4-8 petals) bloom form. Occasional repeat later in the season.
Habit: Arching.
Height of 4' to 5' (120 to 150 cm).
Growing: USDA zone 6b through 9b . Can be trained as a climber. shade tolerant. Disease susceptibility: very disease resistant.

Here is a link that might be useful: Lyda Rose

My guess is rootstock. It might be some sort of R. canina, but the leaves really don't look right for that.

Years ago, I was given a Harison's Yellow that had originally come from Pickering. At the time I was given the rose, it had sucker growth that didn't look familiar. Before I could say anything, the donor said 'Oh, a sucker', and yanked it off. That was more than ten years ago, and this year I finally got a look at the flower. That looks a lot like your rose.

If it bloms only once a year, then its R. canina, sometimes used as a rootstock for grafting onto. This is likely how you came to have it.

The foliage is too matte for 'Lyda Rose', IMO.

Thank you all for your replies :)

I'm not sure of it could be a Rugosa? They are sold around here sometimes so it is a possibility, but I don't know if the leaves/bloom etc fits . . .

Trospero - I would lean towards rootstock too, as it seemed to be own-root (when I moved it) and almost no nursery around here sells ownroot roses. Also it had been in shade and neglected for so long, I wouldn't be at all surprised if the rose died and the rootstock took over.

I do know that it seems to sucker. It will also stretch up really long canes if necessary to try to find some light, but I'm guessing that most roses do that.

I will keep an eye to see if it reblooms or not this summer. I think I remember it setting hips last year as well, but my memory is a bit foggy.

So we're thinking R. Canina? I know that I wouldn't want to grow R.Multiflora as a rose because it seems to be a carrier for serious rose diseases . . . does the same go for R.Canina or would it be fine to grow in the garden?

I think it is typical of a rootstock form of R. canina. The leaf stipules, particularly, are that odd canina type.

This is absolutely not a Rugosa; it has none of the Rugosa traits. I'm pretty sure you are looking at at R. canina which will make a perfectly decent shrub for the garden, albeit a large one, and one that bloom for only a brief period in the early Summer. It is most suitable for a "cottage garden" or wildflower style garden. I suggest you also look at R. glauca, which is a superbly attractive species, even when not in flower. R. glauca makes an attractive, healthy shrub suitable for your climate and requires no care whatsoever.