For example, is "they gave the same rating to the movie" a proper usage?
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You can say of two banks that
But you would be slightly more likely to say
As for "a giving rate" that is an exceedingly odd construction. You might refer to "a given rate" but that would be in a different context.
Edit (after much colloquy in the comments):
Now it's clear you're talking about ratings as in "movie ratings" I would say that the verb to use is give. So it is quite all right to say:
Note that if you use the word same you might be forcing yourself to use the singular: