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Yes, my grandfather's surname was Noth (actully, the 'o' has two dots over it), and since there was no such letter in the English alphabet, it was changed. This is actually quite common, some other examples of names that were changed in a similar fashion are Schroeder, Koenig, and Spoede.
By the way, we pronounce our last name with the 'oe' having a long 'a' sound (pronounced like Naith). Does your family pronounce it this way, or with a long 'o'. I know of other Noeth's not related who pronounce it with the long 'o'.