Team picker command line application

The if/else within the loop are not needed - since they are true only on the first iteration, we can move them before the loop:

def start_team(team_name):
    print(f"Hello {team_name}")
    captain = str.strip(input("Choose your captain: "))
    while not captain:
        captain = input("{team_name} Captain Needed!: ")
    return [captain]

team_1 = start_team("Team 1")
team_2 = start_team("Team 2")


# Loop until both teams have 8 players
while len(team_1) < 8 and len(team_2) < 8:

Alternating choices for each team matters for fairness when humans are choosing. But when we're making a random choice, the order of selection doesn't matter at all. So we can choose all of Team 1's members before those of Team 2. We could do this using random.sample(), but I think a simpler method is just to shuffle the "available" list and allocate the first seven members to Team 1 and the next seven to Team 2:

team_1 = start_team("Team 1")
team_2 = start_team("Team 2")

random.shuffle(available_players)

team_1 += available_players[:7]
team_2 += available_players[7:14]

We might choose to incorporate the selection of players into start_team() (which then needs a different name, of course):

random.shuffle(available_players)

def make_team(team_name):
    print(f"Hello {team_name}")
    captain = str.strip(input("Choose your captain: "))
    while not captain:
        captain = input("{team_name} Captain Needed!: ")
    team = [captain] + available_players[:7]
    del available_players[:7]
    return team

team_1 = make_team("Team 1") 
team_2 = make_team("Team 2")

Moving actions out of the loop

Since picking team captains only happens once per program run, there's no need to have it inside the main loop. I'll use the get_captain() function and the TEAM_SIZE constant from @toolic's answer.

team_1.append(get_captain(1))
team_2.append(get_captain(2))

while len(team_1) < TEAM_SIZE and len(team_2) < TEAM_SIZE:
    # Team 1 selection
    if len(team_1) < TEAM_SIZE:
        pick = random.choice(available_players)
        team_1.append(pick)
        available_players.remove(pick)

    # Team 2 selection
    if len(team_2) < TEAM_SIZE:
        pick = random.choice(available_players)
        team_2.append(pick)
        available_players.remove(pick)

Notice that we no longer need to check if team_1: and if team_2: because these are always true.

Furthermore, the remaining if conditions here are redundant due to the while condition, so we can delete those, too.

team_1.append(get_captain(1))
team_2.append(get_captain(2))

while len(team_1) < TEAM_SIZE and len(team_2) < TEAM_SIZE:
    # Team 1 selection
    pick = random.choice(available_players)
    team_1.append(pick)
    available_players.remove(pick)

    # Team 2 selection
    pick = random.choice(available_players)
    team_2.append(pick)
    available_players.remove(pick)

Separating actions

Picking players for both teams in a single loop is part of why there is so much code duplication. It doesn't matter if players are picked for each team in turns or if team 1 picks seven random players all at once. Let's see what happens when we pick teams in two loops.

while len(team_1) < TEAM_SIZE:
    pick = random.choice(available_players)
    team_1.append(pick)
    available_players.remove(pick)

while len(team_2) < TEAM_SIZE:
    pick = random.choice(available_players)
    team_2.append(pick)
    available_players.remove(pick)

But, because there are 14 players in the available players list, all of the remaining players will be put on team 2. So the second loop can be replaced with team_2.extend(available_players).

while len(team_1) < TEAM_SIZE:
    pick = random.choice(available_players)
    team_1.append(pick)
    available_players.remove(pick)

team_2.extend(available_players)

Replacing loops

Starting here, I'm going to be introducing new functions that can replace loops.

Is there a different way to create team 1 without a loop? There is a random function called sample() that can make multiple random choices without duplicates. So, team 1 can be created by

team_1.extend(random.sample(available_players, TEAM_SIZE - 1))

Now we have a problem forming team 2 since the players on team 1 were not removed from the available players. One way to fix this is to remove them directly.

team_1.extend(random.sample(available_players, TEAM_SIZE - 1))
for player in team_1[1:]: # Skipping the captain
    available_players.remove(player)
team_2.extend(available_players)

To do this with less work, we can use the set container. These can do a lot of work easily and efficiently when we want to add or remove items from collections. In this case, we create a set from the available players, and then subtract the team 1 players to arrive at team 2.

team_2.extend(set(available_players) - set(team_1))

Putting everything together

For the final program, I initialized both team lists with their captains.

import random

def get_captain(team):
    """
    Ask user to input a team captain name for a specified team number.
    Input: team is an integer
    Returns a string
    """
    captain = input(f"Hello Team {team}\nChoose your captain: ")
    while captain == "":
        captain = input(f"Team {team} Captain Needed!: ")
    return captain

# List of all available players
available_players = [
    "Anastasia", "Eli", "Jamal", "Jada", "Theo", "Michelle", "Adam",
    "Rhea", "Charlie", "Jasmine", "Marley", "Kenji", "Sydney", "Yara"
]

TEAM_SIZE = 8

# Lists to store team members
team_1 = [get_captain(1)]
team_2 = [get_captain(2)]

team_1.extend(random.sample(available_players, TEAM_SIZE - 1))
team_2.extend(set(available_players) - set(team_1))

# Game starts when both teams are full
print("All Teams Full:")
print("Team 1:", team_1)
print("Team 2:", team_2)
print("\nIt's Game Time!!")