I am expecting a girl and have a son named [name]Chase[/name] [name]Alexander[/name] [name]Saxon[/name]. I would like to incorporate my grandmother’s name somehow but it is not an absolute. My grandma’s name was [name]Kathryn[/name] [name]Simone[/name]. Some of the names I like are: [name]Charlotte[/name], [name]Claire[/name], [name]Savannah[/name], [name]Georgia[/name] and [name]Lila[/name]. I am Italian and love the name [name]Sophia[/name] or [name]Isabella[/name] but nothing on the top ten, please. I would love some input as nothing is really standing out and I’m getting nervous! 
Here are some ideas based on your list. I’m trying to just give you the options that I really think work together, not just all the possible mixes.
[name]Georgia[/name] [name]Kate[/name] (my favorite!)
[name]Georgia[/name] [name]Kathryn[/name]
[name]Georgia[/name] [name]Simone[/name]
[name]Georgia[/name] [name]Claire[/name]
[name]Georgia[/name] [name]Charlotte[/name] (a bit of a mouthful, I admit)
[name]Charlotte[/name] [name]Claire[/name]
[name]Charlotte[/name] [name]Lily[/name]
[name]Lila[/name] [name]Savannah[/name]
[name]Lila[/name] [name]Simone[/name] (I really like this one too)
[name]Lila[/name] [name]Kathryn[/name]
[name]Lila[/name] [name]Claire[/name]
[name]Lila[/name] [name]Charlotte[/name]
[name]Claire[/name] [name]Simone[/name] / [name]Claire[/name] [name]Simona[/name]
[name]Claire[/name] [name]Charlotte[/name]
[name]Claire[/name] [name]Savannah[/name]
[name]Savannah[/name] [name]Kate[/name]
[name]Savannah[/name] [name]Lily[/name]
[name]Savannah[/name] [name]Claire[/name]
Randoms:
[name]Sophie[/name] [name]Kathryn[/name]
[name]Sophie[/name] [name]Charlotte[/name]
[name]Gianna[/name] [name]Kate[/name]
[name]Gianna[/name] [name]Claire[/name]
My favorite combos, personally, are [name]Georgia[/name] [name]Kate[/name] and [name]Lila[/name] [name]Simone[/name].
[name]Hi[/name], and welcome to NB! You have such wonderful names to work with for your daughter! [name]Kathryn[/name] [name]Simone[/name] is just lovely. [name]May[/name] I ask if [name]Saxon[/name] is your last name, or is it a second middle name for [name]Chase[/name]? Here are some combinations I thought of:
[name]Charlotte[/name] [name]Kathryn[/name] [name]Simone[/name]
[name]Claire[/name] [name]Sophia[/name] [name]Kathryn[/name]
[name]Savannah[/name] [name]Kathryn[/name] [name]Isabella[/name]
[name]Georgia[/name] [name]Claire[/name] [name]Simone[/name]
[name]Lila[/name] [name]Sophie[/name] [name]Kathryn[/name]
[name]Charlotte[/name], [name]Claire[/name], [name]Savannah[/name], [name]Georgia[/name] and [name]Lila[/name]. All gorgeous, all lovely in their own way. I might rule out [name]Charlotte[/name] though due to the shared beginning Ch initials with [name]Chase[/name], but it is not that much of a problem as their sounds are different. [name]Shar[/name] as oposed to Ch.
But here are some more suggestions for first names:
Italian:
[name]Alba[/name]
[name]Allegra[/name]
[name]Bianca[/name]
[name]Elena[/name]
[name]Gemma[/name]
[name]Leandra[/name]
[name]Rosa[/name]
[name]Tullia[/name]
[name]Vanessa[/name]
Other Names:
[name]Ramona[/name]
[name]Isolde[/name]
[name]Amelie[/name]
[name]Clara[/name]
[name]Lucy[/name]
[name]Eliza[/name]
[name]Isadora[/name]
Alternatives to [name]Kathryn[/name]:
[name]Catherine[/name]
[name]Caja[/name]
[name]Catrin[/name]
[name]Carina[/name]
[name]Riona[/name]
[name]Katia[/name]
For the [name]Kathryn[/name]'s meaning “pure”
Amala
[name]Phoebe[/name]
Alternatives to [name]Simone[/name]:
[name]Simona[/name]
[name]Jimena[/name]
Some combo examples:
[name]Alba[/name] [name]Kathryn[/name] [name]Simone[/name]
[name]Vanessa[/name] [name]Kathryn[/name] [name]Simone[/name]
[name]Ramona[/name] [name]Kathryn[/name] [name]Simone[/name]
[name]Caja[/name] [name]Simone[/name]
[name]Catrin[/name] [name]Isabella[/name]/[name]Sophia[/name]
[name]Hope[/name] that helped, I’m happy to suggest more.
I really like [name]Caterina[/name] for you, since it is both related to [name]Kathryn[/name] and is Italian. Plus, I think it’s beautiful and goes well with the other names you listed.
I think [name]Caterina[/name] [name]Simone[/name] is lovely, but I’m biased since my name is [name]Simone[/name] and I love it 
[name]Hi[/name], [name]Saxon[/name] is our last name.
Thank you everyone for the help, great ideas here!!!