Virginia is such a strong name, I'd bet she'd ask people to use that instead of Ruth or Ruthie. I too believe middle names should be no longer, and perhaps shorter than, the first name. Ruth Eileen isn't bad but it depends on your last name which I think to flow would be three syllables and sound ok.
I am one of those that believe in giving your child a name they'd be proud of. The child comes first over honoring grandparents in my book. What if your grandparent was named a name you really didn't like?
My 100 year old mother's name is Ruth Elaine with a one syllable last name starting with a C. It was rather common for her time. I just have a hard time with old fashioned names on kids. That's just me.
My son loved his name because he always knew there wouldn't be anyone else in the class with his name. Course, he liked it too. As newish as I thought it was, I found out that in Texas, it was a very old name from before 100 years ago. But in my son's generation, it was newish and well liked. My daughter loved her name because it was common enough not to be ridiculed for it. She was the sensitive one but of course I didn't know that at the time.
Baby name books give you hints on names that flow as to number of syllables and if it ends in a vowel, the next name should be a ____.
So, what do you know. Do what your heart tells you but do put yourself in your baby's place and know she will carry that name for a lifetime.
And one more thing, my parents expected a tow-headed child like the first two. My hair was almost black. My father's hair was almost black BUT as a child, he had been tow-headed blonde.