Def is repeating when variables are called outside function

I am trying to allow a user to first select if they want to define their name, then outputting either their chosen name or a randomly selected name.
I can play with the positioning of the inputs to either get the function to work fine with n or y but not both.

I want to call the username later on, and when I do so it loops back to ask the user input again.

import random

rando_username = ['Yoda', 'Han', 'Luke', 'General Kenobi', 'Mace Windu', 'Padme', 'Anakin', 'Jar Jar Binks']
random_username = random.choice(rando_username)

user_name_choice = input('Would you like to choose your own name for the duel? y/n')

user_choice = input('What shall we call you?')

def username():
    if user_name_choice == 'y':
        username = user_choice
    else:
        username = random_username
    return username

rando_opponent = ['Darth Vader', 'Darth Sidious', 'Darth Maul', 'Kylo Ren', 'Jabba the Hutt', 'Moff Gideon', 'Jango Fett', 'General Grievous']
random_opponent = random.choice(rando_opponent)

opponent_name_choice = input('Hello there, {}! Would you like to name your enemy? y/n'.format(username()))

opponent_choice = input('What shall we call your enemy?')

def opponent_name():
    if opponent_name_choice == 'y':
        opponent_name = opponent_choice  
    else:
         opponent_name = random_opponent
    return opponent_name

print ('Excellent choice {}, your opponent is {}!'.format(username(), opponent_name()))

You're calling username twice. Try saving username's value to a variable.

Save the username (and opponent name) to a variable. Also put the input('What shall we call you?') in the username function's if user_name_choice == 'y': block, so that it is only called if the the person wants to choose their own name (same goes for the opponent name bit):

import random

rando_username = ['Yoda', 'Han', 'Luke', 'General Kenobi', 'Mace Windu', 'Padme', 'Anakin', 'Jar Jar Binks']
user_name_choice = input('Would you like to choose your own name for the duel? y/n')

def username():
    if user_name_choice == 'y':
        username = input('What shall we call you?')
    else:
        username = random.choice(rando_username)
    return username

name = username()

rando_opponent = ['Darth Vader', 'Darth Sidious', 'Darth Maul', 'Kylo Ren', 'Jabba the Hutt', 'Moff Gideon', 'Jango Fett', 'General Grievous']
opponent_name_choice = input('Hello there, {}! Would you like to name your enemy? y/n'.format(name))


def opponent_name():
    if opponent_name_choice == 'y':
        opponent_name = input('What shall we call your enemy?')
    else:
         opponent_name = random.choice(rando_opponent)
    return opponent_name

print ('Excellent choice {}, your opponent is {}!'.format(name, opponent_name()))

A possible output:

Would you like to choose your own name for the duel? y/nn
Hello there, Jar Jar Binks! Would you like to name your enemy? y/nn
Excellent choice Jar Jar Binks, your opponent is Darth Vader!

(Note that in this example the functions are no longer really necessary, but I left them in case you still need them)

There a few things that I would highlight regarding your code:

• First of all, note that the two methods username and opponent_name do exactly the same thing: they return an entered name if the _choice variables are equal to y, otherwise they will pick a random value from a prefined list. You should collapse them in one method, but let's not go there for now.
• You are always setting a random_username and random_opponent, even when is not needed - i.e. when _choice is equal to y - clearly, you could save some work there,
• In your code, you are taking advantage of the synchronous nature of the input method: in theory, you could even avoid writing username and opponent_name as method, but you could have everything in a monolitic/sequential code
• Note that everytime you are using the () you are calling the method: this could have undesired effects in some situations.

Given this background, I have reorganized your code:

import random

# List of username options
random_username = ['Yoda', 'Han', 'Luke', 'General Kenobi', 'Mace Windu', 'Padme', 'Anakin', 'Jar Jar Binks']

# List of opponents options
random_opponent = ['Darth Vader', 'Darth Sidious', 'Darth Maul', 'Kylo Ren', 'Jabba the Hutt', 'Moff Gideon', 'Jango Fett', 'General Grievous']

def username(user_choice):
    if user_choice == 'y':
        username = input('What shall we call you?')
    else:
        # username random selection happens only if needed
        username = random.choice(random_username)
    return username

def opponent_name(opponent_choice):
    if opponent_choice == 'y':
        opponent_name = input('What shall we call your enemy?') 
    else:
        # opponent name random selection happens only if needed
        opponent_name = random.choice(random_opponent)
    return opponent_name
    
if __name__ == "__main__":
    user_name_choice = input('Would you like to choose your own name for the duel [y/n]? ')
    # username name method called only once and assigned to VARIABLE username
    username = username(user_name_choice)
    
    opponent_name_choice = input(f'Hello there, {username}! Would you like to name your enemy [y/n]? ')
    # opponent_name method called only once and assigned to VARIABLE opponent_name
    opponent_name = opponent_name(opponent_name)
    
    print (f'Excellent choice {username}, your opponent is {opponent_name}!')

As stressed at the first point, username and opponent_name methods do exactly the same thing - you collapse the logic as follows, for example:

def choose_name(your_choice, available_options, you_or_your_enemy):
    if your_choice == 'y':
        return input(f'What shall we call {you_or_your_enemy}? ')
    else:
        return random.choice(available_options)
    
if __name__ == "__main__":
    user_name_choice = input('Would you like to choose your own name for the duel [y/n]? ')
    username = choose_name(user_name_choice, random_username, "you")
    
    opponent_name_choice = input(f'Hello there, {username}! Would you like to name your enemy [y/n]? ')
    opponent_name = choose_name(opponent_name_choice, random_opponent, "your enemy")
    
    print (f'Excellent choice {username}, your opponent is {opponent_name}!')