I wouldn't worry about Ophelia being too close to Olivia.
I just can't get past the Shakepeare character. Ophelia and William together makes it even worse.
I like the way Ophelia sounds but I can't get past the Shakespeare character. I feel the same way about Romeo. Guinevere, Lancelot, and Morgana are also ruined for me. I think that all of these names would make great pet names, however.
I'm ok with Juliet and Arthur because they aren't solely associated with a Shakespeare play or legend.
Edit: Reviving Ophelia, a book on adoloscent girls, was a big deal when I was coming of age so that may be why I am so biased. The book is about how many adoloscent girls lose their sense of self and the psychotherapist compares this phenomenon to Ophelia's character development in Hamlet. This book was a HUGE deal in the mid 90s.