How to run multiple while loops at a time in Pygame

No, that's not the way it goes. You have an application loop so use it. time.sleep, pygame.time.wait() or pygame.time.delay is not the way to wait or delay something in a typical application. The game does not respond while you wait. Use pygame.time.get_ticks() to measure the time.

In pygame the system time can be obtained by calling pygame.time.get_ticks(), which returns the number of milliseconds since pygame.init() was called. See pygame.time module.

Calculate the point in time when the text needs to be changed. Get a new random text and render the text Surface after the current time is greater than the calculated point of time. Calculate a new random point in time which is greater than the current time:

next_render_time = 0 while run: current_time = pygame.time.get_ticks() # [...] if current_time >= next_render_time: currentFace = random.choice(face) faceDisplay = myFont.render(str(currentFace), 1, (0,255,0)) next_render_time = current_time + randint(5, 10) * 1000 screen.fill((0,0,0)) screen.blit(faceDisplay, text_rect) pygame.display.flip() 

The time is multiplied by 1000 (randint(5, 10) * 1000), since the time unit of pygame.time.get_ticks() is milliseconds.

Actually, you can also use a timer event. See How do I use a PyGame timer event?.
In your case, however, the time interval is not constant. It's a bit odd to use a timer event on a dynamically changing interval. I would prefer to use a timer event for an action that needs to be performed at constant intervals. But that's just my opinion.

Complete example:

from random import randint from time import sleep import pygame import pygame.freetype import time import random run = True pygame.init() #faces face = ['^-^', '^v^', '◠◡◠', "'v'", '⁀◡⁀'] talkingFace = ['^o^', '^▽^', '◠▽◠', "'▽'", '⁀ᗢ⁀'] currentFace = random.choice(face) #background screen = pygame.display.set_mode((800,600)) #font and size myFont = pygame.font.Font('unifont.ttf', 100) #face render faceDisplay = myFont.render(str(currentFace), 1, (0,255,0)) #center and draw face text_rect = faceDisplay.get_rect(center=(800/2, 600/2)) next_render_time = 0 #prevent crashes while run: current_time = pygame.time.get_ticks() for e in pygame.event.get(): if e.type == pygame.QUIT: run = False if current_time >= next_render_time: currentFace = random.choice(face) faceDisplay = myFont.render(str(currentFace), 1, (0,255,0)) next_render_time = current_time + randint(5, 10) * 1000 screen.fill((0,0,0)) screen.blit(faceDisplay, text_rect) pygame.display.flip()