I think
Rose is a better name, partly because it is not a nickname and not just a flower name.
But also because
Lily, being a repeated syllable, sounds a little bit cutesy.
Lily's not bad, it's just not better than
Rose.
Rose Marina
This question always makes me think of the
Christina Rossetti poem that begins
The lily has a smooth stalk,
Will never hurt your hand;
But the rose upon her briar
Is lady of the land.
- mirfak