Q1: Who made up the name "Monte Carlo Method"?
A1: It was named by John Von Neumann, Stanislaw Ulam, and Nicholas Metropolis. They coined the name together while working on a nuclear weapons project in the Los Alamos National Laboratory.

Q2: Which of the many Bernoulli is the Bernoulli random variable named after?
A2: The Bernoulli random variable is named after Jacob Bernoulli (1655-1705).

Q3: Optional / Extra credit (Up to 10 brownie points): Find an interesting application to biology of Gambler's Ruin.
A3: It predicts that eventual every species will go extinct. It also shows that common descent is the result of pretty much any long-term process that involves speciation and extinction and is not dependent on natural selection but rather on the probabilities (still, adaptation is dependent on natural selection, therefore natural selection still holds true as an evolutionary mechanism).
(http://pierce.wesleyancollege.edu/faculty/brhoades/courses/Ouzelmanual/gamblersruin.html)