I'm happy for you that you managed to find a book that spells it your way. I think your action linking to Britannica speaks for itself. Regardless, it's spelled Eratosthenes. It's a translated name, so we understand some people are going to spell it one way or another, especially when referring to older sources, but there is still a most correct way to spell the name.
There is in fact one and only one way to spell Eratosthenes, for the following simple yet very compelling reason :
in ancient Greek most of the names had a meaning, more or less in relation with the concerned person or one of his ancestors. Now "Erathostenes" has no specific meaning (at least to my knowledge), meanwhile "Eratosthenes" can split into its two components "Erato-sthenes", which means "strength of love" (or strengthened by love).
With such a mane, there is no wonder he was such a gifted and famous philosopher!....,