Our dd2 is named after my dh's grandma and my Gran.
Her first name is Rachel - which was dh's Grandma's 1st name althought she was always known as Ruby (Robina), form her middle name. She died, sadly, just 2 weeks before dd2 was born.
Her middle name is Jessie. My Gran always hated her name - wanted to be Jessica, but her full name is Jessie (I think this is where my about shortened names comes from ). SO because she didn't like her name (she was always Jess) she was delighted we used it a a middle name and even then said "I wish I had a better name to give that Bairn!" But she was secretly delighted.
I only found out later that Jessie is also used as a short version of Janet, which is my other Grandma's name (though she is too demented now to even know I have children, sadly).
My Gran died last year, and I am now delighted in every way that dd2 bears her name .. and in fact, it might seem sad, but it appears that dd2's earliest memory is visiting "GG" (Great Gran) the day before she died - she now talks a lot about "my GG in the pretty blue dress" (nurses were fab, she was wearing her fave blue nightie, with hair done and nails all red, when we went to visit, even though she was pretty much unconscious. They even had her dire favourite accordion music playing!).
If you can get round it somehow, using both names would, I think, be nice. I am glad that "Rachel Jessie" gives so much pleasure to the family who are still here.