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In Star Trek Beyond they destroy the Enterprise NCC-1701-A. As such, why is the new ship being built also called the NCC-1701-A instead of -B, as in the original movies?
Unfortunately, your original assumption is incorrect.
The ship that was destroyed was NCC-1701 not NCC-1701-A
So, when the new ship is constructed at the end of ST:B IT was designated NCC-1701-A.
At least originally, the full letter jump has always accompanied a complete change in the class of starship.
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