Well on the one hand, Runeterra's a planet and there's likely tons of people called Daisy. Also Daisy was called Daisy cuz of the daisy's that grew on her, rather than anything else. It's likely a coincidence.
On the other hand:
- The golem finds Daisy caught in the river, and goes to help. Sadly Daisy's already dead, and the river's waters harm the golem, leaving it wounded and in need of help.
- Ivern stumbles on the scene, and sees that he can help things along as nature intends. Just like he did with the Shagyak in "Gift of Venom" he accelerates the natural decay of Daisy's corpse, prompting her body to rot until her remains have become a part of the pebble'd beach.
- He takes one of these pebbles and fashions it in to a heart for the golem. As part of the code of mineral organisms the golem follows Ivern from this point on.
- The daisy's that grew on the golem were because of Daisy's life force having permeated the stone. A coincidence of nature or nature's way of recognising how life changed and who's lives were changed? Hard to say, but the golem is dubbed Daisy for them.
A little ramble from me at 6 in the morning, but eh, it's what I do really. I personally lean towards the former, cuz I feel like Ivern's story gets a bit cheapened by the Daisy connection, considering his relationship with the golem Daisy is about his selflessness, rather than preserving someone's life that was either on their way out or already dead. Ivern's about going about things in natures way, after all.