I think Gillian is a really soft and pretty name. I prefer it spelled with a G than a J too. It gives me the same feel as names like Ava, Claire, Genevieve, and Imogen, and I think it goes well with names like those. Gillian Claire would be really pretty. Some others:
Gillian Abigail
Gillian Edith
Gillian Fiona
Gillian Iona
Gillian Isobel
Gillian Nora
Gillian Sarah
Gillian Violet