I would think the crew would be the strongest link anyone would have to TOS?
If you can lose them, why exactly would the ship name be so crucial?
Because we did
lose them. They weren't the crew featured in TNG, nor was the show in the same era. But having a ship named Enterprise
was a way of continuing things forward a century, yet still maintaining an immediate and easily accessible link to TOS.
Any new series will likely be set on an Enterprise.
I'd bet money on it. I think the only way it wouldn't is if the new series was intended to be a same-era spinoff of the current movies already featuring the Enterprise