Lorya, Naturebond Fluidling

When Lorya, The Naturebond Fluidling enters
the battlefield you may have Lora become a copy
of target blue or green creature exept it has
"whenever this creature deals damage, you may
search your library for creature that shares a type
with it that costs less and put it in the battlefield."
"As the champion of nature, the creatures have come
to bond with me. As such they have given me a name.
I have never had a name before"