Sounds like lovely ideas to me. For me, it is still a fantasy to try something like that. But I will one day. Your quilt is lovely. Hope to see it after you have quilted it.

Me I would match to the area of color. Or go neutral. Beautiful quilt.

My vote is for tan or taupe and a bit more fancy quilting in the sqaures.

A beautiful quilt; beautiful fabric. No suggestion for quilting.

Personally I feel that the quilting, while it can enhance greatly, should not compete with, but compliment, the quilt itself. You have a beautiful quilt made and I think you would distract from the overall effect if you used colors in the white area. I have seen award winning quilts which, the more you look, the more you see. At first most of us don't see the quilting, but upon closer inspection it is a thrill to discover the beautiful designs quilted in. It makes the quilt a venture of discovery.

Nice top. I would FMQ a floral design in off white on the star centers and the other squares, not quilt the star points and something like a vine on the off white with an old rose. The outer border I'd do with a deep rose feather with off white vines on the inner border. Of course, that's me. Do something you are comfortable with that complements the pattern elements.

The first color thread I would try would be a tan/taupe variegated thread...I would pull off a bunch on the burgundy pink area to see how it looks there. You can tell how the color will look by doing that.

As for the quilting, I am always at a loss on 'how' to quilt something. I have a baby quilt that has been pin basted and waiting for 10 days and thinking I am going to end up just meandering simply because I cannot make up my mind what to do and it needs to be done by the end of April.

as to HOW to quilt it,

In the last few years I have become a fan of variegated thread, cotton or Rayon for my quilts. I especially like using the Rayon thread on some of my simpler quilts just to give it a little zip. Whatever you do, it will be beautiful, just like your quilt.

I love the quilt and wonder if there is a pattern name?

If I were doing this quilt I would do a cream color for the whole quilt, any way I quilted it. It is a very pretty quilt and wouldn't want quilting to distract from the pieced work. A cream would not be invisible but not overwhelm the beauty of the pattern. If special quilting were to be used in the background area it will be pretty without showing to much.
peace