Should there be a fallacy for not all evidence supporting hypothesis?

I know there's the cherry-picking fallacy where you just pick an item or two without consideration of context or other evidence but I wonder if there should be a fallacy that simply says, "Not all the evidence supports the hypothesis" so regardless of the item/s put forward as not all the evidence supports the hypothesis it is invalid. For an hypothesis to be correct all the available evidence must support it. I guess cherry-picking works fine but I wonder if a fallacy that is strictly based on the fact that all the evidence must support an hypothesis for it to be correct another fallacy could be created.

No, thats not how the scientific method works. Hypothesis aren't meant to be correct, they are meant to be falsified so that they can become theories. 

Hypothesis are testable educated guesses. They need to be testable so that they can be falsified via the  testing process. The hypothesis that hasn't been falsified by testing is left standing after all the other hypothesis have been falsified. Only then can the hypothesis that is left standing graduate into a scientific theory.   

If someone choses to believe a falsified hypothesis over the theory (the hypothesis that hasn't been falsified) due to cherry picking (cognitive bias) then yes, it would be a cherry picking fallacy. 

"Should there be a fallacy for not all evidence supporting hypothesis?"

All evidence not supporting a hypothesis is not a fallacy. Someone claiming that the hypothesis is supported by all the evidence when it is not is also not a fallacy, its just factually incorrect. Someone claiming that the hypothesis is supported by all the evidence because of cherry picked x y and z, now that is a fallacy (cherry picking fallacy.)

Cherry picking fallacies are usually committed due to an underlining cognitive bias that emotionally favors the hypothesis.

For an hypothesis to be correct all the available evidence must support it.

Actually, an hypothesis is either falsified, or has yet to be falsified. There could be plenty of evidence that does not support an hypothesis; but this can simply be irrelevant rather than dis-confirming. There could be evidence that points to a competing, conflicting hypothesis, but still isn't evidence that falsifies the other hypothesis.

I am not quite sure here what you are proposing is fallacious. Can you provide an example as used in argumentation?

No.  

First, because a hypothesis is almost never ready for that sort of test.  The single example imo* is the simple form of Earth's gravity, which proceeded from the commonplace observation that stuff you drop falls to Earth, so that if the hypothesis were "every solid thing on Earth is attracted to it", there would be no evidence to contradict it, since nothing condensed to solid ever simply rises if released.  The Newton/apple story is apocryphal of course, but a single apple that, freed from its tree. went higher than its connecting point, would have demolished the hypothesis.

*It is surprisingly complicated to write the hypothesis so it includes all the possible exceptions in a general and concise way. 

Let me propose that the hypothesis of gravity is in fact the exception that proves the rule.

For almost all (or all, that I know of) hypotheses, we are constrained by our ability to detect or recognize an effect and are often also limited by our ability to detect or recognize a possible cause.  If we wait for perfect knowledge, we're subject to the Nirvana Fallacy  and the demand that all evidence support the hypothesis, as proposed by the question, is then that fallacy, 

In the 3-400 years since the Newton version of the gravity hypothesis, we had no basis for denying it, and might have been tempted to assert it as  beyond all shadow of a doubt, a platinum standard only possibly achieved by the acceptance of thermodynamics' conclusion that there can be (not merely are, but can be) no perpetual motion machine.  Along came Albert, (the only scientist as famous by one name as a modern singer), and oops, the Newton apple cart is upset.

Our courts do not demand "beyond all doubt", in part because our data is incomplete, imperfect, perhaps even biased, but rather asks for proof "beyond a reasonable doubt" to convict a suspect.

Science's demands are harder, but a demand that there be no exceptions in the data is itself a fallacy, so in the name of protecting from the Cherry Picking fallacy, it would institute its own Nirvana Fallacy.