Indie - I'm not keen on Indie, I think Indie is just too nickname-y also I find Indie a little too informal next to Imogen. I really dislike this choice. Indie just isn't my thing.
Eleanor - Ah a beautiful classic, rich in style and elegance. I adore Eleanor she's beautiful and sounds so pretty with Imogen.
Esther - I think Esther is very wholesome and sweet. Esther sounds lovely as well I also love the connotations, but I don't think Esther works with Imogen. They just sound too different.
Charlotte - I love this choice, Charlotte is such a sweet, wholesome name. I also love the nickname Lottie. Charlotte is a beautiful classic. She works so well with Imogen. Together Imogen & Charlotte sound very British and cute together.
Ivy - Even though I love Ivy she's very cute and humble but I dislike Ivy with Imogen. Firstly having two names with the same initial could be limiting, for example a sibling set like Fay, Fiona, and Cora seems strange the 'C' seems strange next too the two 'F' names.
Brooklyn - I dislike Brooklyn, for me Brooklyn is trashy and totally ruins Imogen.
Lola - Ah she's such lovely name, with a really sweet Spanish feel. I love how Imogen sounds with Lola. The name sounds so gorgeous together. Lola & Imogen sound beautiful together.
Talulah - I dislike this spelling I prefer Tallulah. Tallulah is a very spunky choice but I dislike how Imogen & Tallulah sound together.
Rosalie & Imogen
Louisa & Imogen
Clara & Imogen
Beatrix & Imogen
Elena & Imogen (eh LAY nuh)
Penelope & Imogen
Pearl & Imogen
Augusta & Imogen
Ophelia & Imogen
Juliet & Imogen
Scarlett & Imogen
The only ones that seem to go with Imogen are Eleanor and Esther.
Indie, Brooklyn and Lola clash with Imogen. Ivy could work, but then you might be stuck with an I theme to continue if you have more children. Another name with a quirky vibe to it would be better...and you said you wanted something not common.
Charlotte is super common. Since you named your daughter Imogen, I would have thought that you liked old-fashioned names.
Dolores - Lola comes from Dolores so you could use it as a nickname
Rosalind or Rosamund
A Dora name: Eudora, Isadora, Pandora, Theodora, Dorothea
Louisa or Louise