the correct answer in this case is: don't do this. (and yes, it's possible to do this, but again, don't do this)
Essentially, your user should not even need to be made aware of what variables are, and should absolutely not be controlling what variable names are created in your code dynamically for your objects of these classes.
So, one actual solution that bypasses this issue is to just use a dictionary. take a string from user, that's a key in a dictionary. initialize your class against the key in the dictionary, and just use the key to access the class.
Another, perhaps better solution, is to just have your class take an extra name attribute. when you need to display the name the user entered for the class, you access it on the attribute. Then you do not even need to use a dictionary, you just create the class with your own variable name internally, but always display the user entered name from it's attribute. This separates concerns between what the user knows and what the programmer should deal with.
# Recommended solution
class Project:
def __init__(self, name, other_params):
self.name = name
self.other_params = other_params
def some_method(self, extra_args):
pass
class Client:
def __init__(self, name, other_params):
self.name = name
self.other_params = other_params
def some_method(self, extra_args):
pass
# these can come from your gui instead of input, doesn't matter
project_user_input = input("enter project name: ")
# these can come from your gui instead of input, doesn't matter
client_user_input = input("enter client name: ")
# make the actual objects, your variable names are internal to you,
# and the names themselves should not be tied to business logic.
# use the .name method to access the user-facing names.
project_obj = Project(name=project_user_input, other_params=42)
client_obj = Client(name=client_user_input, other_params=100)
# you can always access user facing names as necessary.
print(f"the project has the name: {project_obj.name}")
print(f"the client has the name: {client_obj.name}")