You may reject the null hypothesis but you never accept it, you only fail to reject it. That is, you may conclude that the evidence (observations) is not sufficiently strong to reject the null hypothesis, but you do not embrace
the null hypothesis and accept it.
For example, in a clinical trial to test whether a certain medicine is
efficacious, the null hypothesis is that the medicine is not effective.
If the evidence is strong that the medicine is effective, you reject
the null. If the evidence is weak, you say that there is not sufficient
evidence to reject the null hypothesis. You do not declare thst
the medicine is ineffective (accept the null), just that there is
not enough evidence to say that it is effective (do not reject the null).
In the case of a point null such as $\mu = 0$, you can say with some
confidence that $\mu \neq 0$ if the evidence points that way, but in
the presence of weak evidence, a savvy statistician would say that
there is not sufficient evidence to conclude that $\mu \neq 0$
rather than proclaim to all the world that $\mu = 0$ as proven
by the test just concluded. After all, the actual value of
$\mu$ might be ever so slightly different from $\mu\ldots$