NameGenChallenge.py

import random




def genName():

    boyNames = {0: "Jack",1: "Andrew", 2: "Mike",3: "Terry",4: "Torvald", 5: "Gatsby"}
    girlNames = {0: "Alice", 1: "Hana", 2: "Clare", 3: "Janet", 4: "Daisy"}
    genderList = {0: "M", 1: "F"}
    randGender = random.randrange(0, 2)
    randGirlName = random.randrange(0, len(girlNames))
    randBoyName = random.randrange(0, len(boyNames))

    askGender = raw_input("What Name Gender would you like? (m/f) (enter 'r' for random)")
    askGender = askGender.lower()

    if askGender != "m":
        if askGender != "r":
            if askGender !="f":
                print "please enter 'M' ,'F', or 'R' to initiate the Random Name Generator"
    if askGender == "r":
        if genderList[randGender] == "m":
            return boyNames[randBoyName]
        else:
            return girlNames[randGirlName]

    if askGender == "m":
        return boyNames[randBoyName]
    elif askGender == "f":
        return girlNames[randGirlName]



print "Welcome to the Simple Random Name Generator by Liquid Think!"
print genName()

Rather than bothering with selecting an element by a random index from random.randrange, you can use random.choice(), for example:

if gender == "male":
    return random.choice(boyNames)
elif gender == "female":
    return random.choice(girlNames)

That omits the sample method johnzeringue mentioned above and arguably adds to the readability of the code.
Hope I could help!

leaen, I knew about about random.choice at the time of writing but wanted to keep my post about coding instead of Python libraries.

Thanks for adding that, though. It's good to know what's already been written for you when you progress to larger projects.

Thank all!