I need a function where the input is a list of probability values from 0 to 1, and the output is the chance that one of these probabilities comes out true.
eg.
0.5 + 0.5 = 0.75
0.9 + 0.9 + 0.9 = 0.999
Is there a standard name for this function/method/operation?
On
Assuming $A,B$ are independent events, you can compute the calculation as $$\operatorname{P}(A\text{ or }B)=\operatorname{P}(A)+\operatorname{P}(B)-\operatorname{P}(A)\cdot \operatorname{P}(B)$$You should be able to see how this works by considering how "or" and "and" are represented on a logical Venn diagram and that $\operatorname{P}(A\text{ and }B)=\operatorname{P}(A)\cdot \operatorname{P}(B)$, for independent events.
Denoting the operator by the symbol $\vee$, this coincides with your examples, $0.5\vee0.5=0.5+0.5-0.5^2=0.75$ and $(0.9\vee0.9)\vee 0.9=0.999$. This last example shows how you can use multiple arguments by iteratively using the aforementioned relation. It doesn't matter which order you perform each $\vee$ in since it is associative.
The standard name is "or" or "disjunction" but I'm confused by why you're asking that since you put it in your question's title.
In general, the operator applied to all elements of a set $\{x_i\}_{1\le i\le n}$ would equal $$x_{1}+\left(1-x_{1}\right)x_{2}+\left(1-x_{1}\right)\left(1-x_{2}\right)x_{3}+...+\left(\left(1-x_{1}\right)\left(1-x_{2}\right)\left(1-x_{3}\right)...\right)x_{n} \\ =\sum_{i=1}^nx_i\prod_{j=1}^{i-1}(1-x_j)$$
It is the complementary cumulative distribution function of the maximum of independent (but not necessarily identical) Bernoulli random variables: $$1-\prod_i (1-p_i)$$