I actually prefer
Rose as a name, but I think
Rose works better as a middle name for girls and
Rosemary might work better as a first name. Its hard to get good combos starting with
Rose maybe, but easier to match it as a mn to other first names.
I think if you switched to
Eleanor Rose it would flow better imo.
So of the two I prefer
Rosemary Kate
Have you also considered
Roseanne and
Rosalind?