hostname = socket.gethostbyaddr(tuple(iplist))
                 ^^^^^^^^^^^^^^^^^^^^^^
TypeError: gethostbyaddr() argument 1 must be str, bytes or bytearray, not tuple

 import socket
from PyQt6 import QtCore, QtGui, QtWidgets
import ipaddress
 
# проверка на валидацию IP адресов
def ip_checkv4(self):
        ip1 = "10.62.39.1"
        ip2 = "10.62.39.5"
 
        if(ip1 == "" and ip2 == ""):
            print("Начальный и конечный IP-адреса должны быть введены.")
        elif(ipaddress.ip_address(ip1) and ipaddress.ip_address(ip2)):
            ipaddress1 = ip1.split(".") # ['10', '62', '39', '1']
            ipaddress2 = ip2.split(".") #['10', '62', '39', '5']
            if(ipaddress1[:3] == ipaddress2[:3]): # проверка на совпадение первых трех октетов ['10', '62', '39']['10', '62', '39']
                if(ipaddress1[3] < ipaddress2[3]): # если четвертый октет меньше, то выводим диапазон
                    # hostname = socket.gethostbyaddr(ip1)[0]
                    iplist = []
                    ipcur = ipaddress.ip_address(ip1)
                    while ipcur <= ipaddress.ip_address(ip2):
                        iplist.append(str(ipcur))
                        ipcur += 1
                        hostname = socket.gethostbyaddr(ipcur)
                    print(f"Доменное имя для {iplist} как {hostname}")
                else:
                    print("Четвертый октет первого IP адреса должен быть меньше четвертого октета второго IP адреса.")
            else:
                print("Первые три октета IP-адресов не совпадают.")
        else:
            print("Некорректно введены IP адреса.")

  
import ipaddress
import socket
 
def make_ip_range(start, end):
    out = []
    ipcur = ipaddress.ip_address(start)
    while ipcur <= ipaddress.ip_address(end):
        out.append(str(ipcur))
        ipcur += 1
    return out
 
def get_domain_name(ip):
    try:
        out = socket.gethostbyaddr(ip)[0]
    except socket.herror:
        out = None
    return out
 
def f():
    ipstart = '10.62.39.1'
    ipend = '10.62.39.12'
    iplist = make_ip_range(ipstart, ipend)
    namelist = list(map(get_domain_name, iplist))
    print(iplist)
    print(namelist)
 
f()

  
>>> import ipaddress
>>> import socket
>>> 
>>> def make_ip_range(start, end):
...     out = []
...     ipcur = ipaddress.ip_address(start)
...     while ipcur <= ipaddress.ip_address(end):
...         out.append(str(ipcur))
...         ipcur += 1
...     return out
... 
>>> def get_domain_name(ip):
...     try:
...         out = 'name for ' + str(ip)#socket.gethostbyaddr(ip)[0]
...     except socket.herror:
...         out = None
...     return out
... 
>>> def f():
...     ipstart = '10.62.39.1'
...     ipend = '10.62.39.12'
...     iplist = make_ip_range(ipstart, ipend)
...     namelist = list(map(get_domain_name, iplist))
...     print(iplist)
...     print(namelist)
... 
>>> f()
['10.62.39.1', '10.62.39.2', '10.62.39.3', '10.62.39.4', '10.62.39.5', '10.62.39.6', '10.62.39.7', '10.62.39.8', '10.62.39.9', '10.62.39.10', '10.62.39.11', '10.62.39.12']
['name for 10.62.39.1', 'name for 10.62.39.2', 'name for 10.62.39.3', 'name for 10.62.39.4', 'name for 10.62.39.5', 'name for 10.62.39.6', 'name for 10.62.39.7', 'name for 10.62.39.8', 'name for 10.62.39.9', 'name for 10.62.39.10', 'name for 10.62.39.11', 'name for 10.62.39.12']
>>>

 iplist = []
hostname = []
ipcur = ipaddress.ip_address(ip1)
while ipcur <= ipaddress.ip_address(ip2):
    iplist.append(str(ipcur))
    ipcur += 1
    addr = socket.gethostbyaddr(str(ipcur))[0]
    hostname.append(addr)
print(f"Domain names {iplist} as {hostname}")

 def ip_checkv4(self):
        ip1 = "10.62.39.1"
        ip2 = "10.62.39.5"
        if(ip1 == "" and ip2 == ""):
            print("Начальный и конечный IP-адреса должны быть введены.")
        elif(ipaddress.ip_address(ip1) and ipaddress.ip_address(ip2)):
            ipaddress1 = ip1.split(".")
            ipaddress2 = ip2.split(".")
            if(ipaddress1[:3] == ipaddress2[:3]): # проверка на совпадение первых трех октетов
                if(ipaddress1[3] < ipaddress2[3]): # если четвертый октет меньше, то выводим диапазон
                    iplist = []
                    hostname = []
                    ipcur = ipaddress.ip_address(ip1)
                    while ipcur <= ipaddress.ip_address(ip2):
                        iplist.append(str(ipcur))
                        ipcur += 1
                        addr = socket.gethostbyaddr(str(ipcur))[0]
                        hostname.append(addr)
                    print(f"IP-адресу {iplist} соответствует доменное имя {hostname}")
                else:
                    print("Четвертый октет первого IP адреса должен быть меньше четвертого октета второго IP адреса.")
            else:
                print("Первые три октета IP-адресов не совпадают.")
        else:
            print("Некорректно введены IP адреса.")

 addr = socket.gethostbyaddr(str(ipcur))[0]
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
socket.herror: [Errno 11004] host not found

  
>>> import socket
>>> 
>>> def get_domain_name(ip):
...     try:
...         out = socket.gethostbyaddr(ip)[0]
...     except socket.herror:
...         out = None
...     return out
... 
>>> def test_address(address):
...     if get_domain_name(address) is not None:
...         print(address, 'доступен')
...     else:
...         print(address, 'недоступен')
... 
>>> test_address('127.0.0.1')
127.0.0.1 доступен
>>> test_address('123.0.0.1')
123.0.0.1 недоступен
>>>