Assuming you want to do this for more than one person, you could store each person as a dictionary like Dicts in a list. This function should do the splitting by spaces and also allows for cases where someone doesn't have a title, i.e., just a first and last name.
def split_names(dict_list):
    l = []
    for dict_i in dict_list:
        new_list = list(dict_i.values())[0].split()
        if len(new_list) == 2:
            l.append(
                {'First': new_list[0],
                 'Last': new_list[1]}
            )
        else:
            l.append(
                {'Title': new_list[0],
                 'First': new_list[1],
                 'Last': new_list[2]}
            )
    return l
Then,
Dicts = {'Name': 'Dr. John Smith'}
split_names(Dicts)
[{'Title': 'Dr.', 'First': 'John', 'Last': 'Smith'}]
Or more generally:
Dicts = [{'Name': 'Dr. John Smith'}, {'Name': 'Mr. Mike Jones'}, {'Name': 'John Doe'}]
split_names(Dicts)
[{'Title': 'Dr.', 'First': 'John', 'Last': 'Smith'},
 {'Title': 'Mr.', 'First': 'Mike', 'Last': 'Jones'},
 {'First': 'John', 'Last': 'Doe'}]