Having researched my Grenfell family for 25 years I think I
have come across every variant of the name.One family had
children baptised with five different variant names over a decade and it was obviously what the clerk heard them say, or what he knew about local names that determined what he wrote
There are several instances in the early St Just records where
one arm of the family used GL and another GR in their names.
You do not mention the date that Alice was born - there were
Alice Grenfells and families of Hosking(n) in St Ives!
Might be worth you giving us the details.
Jill in Sydney