Personally, I don't like the name Honor, however it's spelt.
But, like OP, I thought that it was a virtue name that used an American spelling of the word. I didn't realise it was unconnected to the word Honour.
Other 6 letter names you might like, OP:
Ariana, Alexia, Alicia, Angela, Andrea, Annika, Bryony, Bonnie, Bronte, Connie, Callie, Carrie, Cassie, Claire, Daphne, Darcey, Esther, Gracie, Hannah, Hallie, Isabel, Juliet, Joelle, Louisa, Leonie, Martha, Maisie, Monica, Nicole, Olivia, Pamela, Rachel, Rowena, Ramona, Serena, Saskia, Selina, Stella, Summer, Sophia, Tamsin, Teresa, Verity, Violet, Willow, Xanthe, Yasmin