A straggler with green eyes stumbles into the last remaining human outpost. The green eye trait did not exist in the outpost before her arrival, but it does now. What is the name of this mechanism of evolution?

Gene flow is the name of mechanism of evolution.

Explanation:

Gene flow in biology and population genetics, is defined as the transfer of a specific genetic variation from a part of the population to another. Once this rate of flowing of genes from one population to another is high enough, it then leads to a them achieving a similar nearly equivalent allele frequencies, which leads to them becoming effectively a single population as it goes on.

In the example given in the question, the one that fits the spot the most will be gene flow due to the genes flowing from the straggler into the outpost, leading to the existence of these alleles.