Socket chat room in Python
host = input(str("Please enter the hostname of the server : "))
...
message = input(str("Please enter your message: "))


can be changed to simply:

message = input("Please enter your message: ")
...
host = input("Please enter the hostname of the server : ")


since there is no need to cast a string to a string.

while 1:


is fine, but is more readable as:

while True:


Having print statements like the following:

print("")


is redundant. If you want an extra newline after a print statement; Add "\n" to the end of the preceding print statements to remove a function call, and reduce code clutter. E.G:

print("Sent\n")


This is more of a personal preference, but fstring formatting is more readable  than the following:

print(s_name, ":" ,message)


should be:

print( f"{s_name}: {message}" )