This rose was labeled "Fame" but clearly it's not. The bloom is very double and quartered. It is a dark slightly purplish red. The leaves are a medium matte green. The buds are sort of flattened. Any suggestions?

Wow, it's quite beautiful! A bit more info might help.
1) How big are the blooms?
2) Does it repeat?
3) What is the frame of the plant like - long sticks like HPs and HT's or more branched like Portlands and floribundas?
4) It looks like the leaves are really close to the bud on the stem; is that right?

The blooms are quite small, about 2'' across and flatish. I'll check it out more tomorrow. I also can count the petals, get a close up of the thorns... anything else? Oh, yes it is only faintly fragrant if at all.

The size of the flowers and their shape suggest portland as a class. Leaves close to the flowers is also suggestive, as is their dark color and smooth texture. The most commonly grown reddish rose in that class is Rose de Rescht.
http://www.helpmefind.com/rose...
Three problems with that guess are that:
1) it's supposed to have strong fragrance,
2) it has a reputation of being well branched and shrubby,
3) the flowers don't look quite exactly the same.

But after looking at all the photos of red portlands at HelpMeFind, I can't find one in this color that is closer to the shape. And, in fact, that beautiful dark green foliage that RdeR has, seems to belong to your rose and be kind of rare in old roses.

From what I can see I couldn't rule out the gallica Charles de Mills http://www.helpmefind.com/rose...
Or Louise Phillip
http://www.helpmefind.com/rose...
Or even Kean (aka Shakespeare)
http://www.helpmefind.com/rose...

Maybe it could be a gallica. Gallicas tend to make long canes as your rose does; but the leaves of many Gallicas have more texture and tend to be brighter, lighter, or yellower. I'll list some less likely ones just for the fun of looking at them.
http://www.helpmefind.com/rose...
http://www.helpmefind.com/rose...
http://www.helpmefind.com/rose...
http://www.helpmefind.com/rose...
http://www.helpmefind.com/rose...
http://www.helpmefind.com/rose...
http://www.helpmefind.com/rose...
http://www.helpmefind.com/rose...

I've not researched hybrid perpetuals on the assumption that its small flowers preclude that. Same for English Roses.

If it repeats, it's definitely not a gallica.
If it doesn't repeat it's definitely not Rose de Rescht. Nor is it a hybrid perpetual or an english rose.

So far Louise Phillip looks the most likely. This rose does repeat bloom. The leaf color and cane characteristics are not uniform. I will get a clear picture if I can tomorrow. This is getting more and more interesting.

What a great post, Steve. I loved clicking on all of those pictures.

Thanks Zuzu. I had fun with that, too. Seems like we still haven't got the right rose. It's one that looks like the gallica Louis Phillip in stature, flower form, and color; but it repeats.

It has been too windy to get any good pictures, but here are a few more details: the leaves do come very close to the buds. There is one 3-leaflet group then all 5s. The flower stem is only about 1" long. The new growth is almost thornless, the older canes have small ones. The canes are generally upright with little branching and blooms develop all along them not just at the tip - almost could be a climber. .The blooms are very densely petaled and never open to expose their centers.The leaves are not all the same shade of green. Some being quite light, none really dark or shiny. Thanks, Steve, the gallica collection was fun to look at and some do look quite a lot like my mystery.

What nursery did you get it from?

It was a gift from my son who brought it from the LA area. It may have been from a big box store, in fact probably was. - I know that is no help, except it possibly eliminates the more esoteric roses.