Let me tell you a story...
DS2 was born on a Sunday night. We had named DS1 quickly and were happy with the name so my DM expected the same with DS2. We weren't sure from our shortlist but DM wanted to be able to announce her new grandson's name at her hobby group on the Monday evening. She visited first thing Monday morning telling us that it was a shame he hadn't yet got a name (he was 7 hours old). She then phoned several times that day to check whether we had decided. I felt under pressure and we chose DH's favourite which I was quite happy with. I rang to tell her with minutes to go before her deadline as she went out to her hobby group.
DF answered the phone, heard the name and went quiet except to say, "You'd better tell your mother!" DM came to phone, heard the name and exploded with a 20 minute tirade on why it was inappropriate, and unacceptable, and she wouldn't be calling him that. The name was perfectly ordinary, if not often chosen at that time (more popular since).
I came off the phone in tears, with her saying that if she had to tell her hobby group that name she would be explaining how tired I must have been to come up with it. In my desperation I told her in that case to hold fire and I would talk more about it with DH.
DH was very unhappy, not only at the name debacle, but at how upset I was. However, we talked more and decided that although it wasn't for my DM to choose our son's name, it didn't feel fair on him that she would introduce him to people throughout his childhood with an apology for his name (and she would have). We changed the name which took us three days and said we would never tell DS2 about what happened.
DM was happy with the new name and we grew accustomed to it. We didn't get our wish of him never knowing though. As soon as he was old enough to understand she told him the story by telling a complete stranger (at a stately home - oh the irony) in front of him and me.
That is our story. Think very hard about changing Susie's name. It is beautiful. Think hard about whether you want a little Flo though. If not, change to Mia or Rose or anything else you love. Please don't take second best for your little one. You will remember every time you have to write her name on anything. You'll remember as you apply for a passport, and you'll remember as she makes her wedding vows. She is your daughter. Make your own choice for her; it is one of the first of many many more.
P.S. The little girl I never had would have been Susie. I absolutely love it.
And a big congratulations to you and your DH on your new DD 