The scope of an alias command is the shell it is run in. When that shell exits and a new one starts, it will not have the alias defined.
The way persistent customization is provided to shells is with shell scripts that are run when the shell first starts up. For example, bash will run either or both of .bash_profile and .bashrcdepending on how it is invoked and other local configuration. Refer to the documentation for the shell you're interested in interacting with for all of the specific details of how it handles this.
If you want persistent configuration changes to a shell, you need to modify the shell's startup scripts.
os.system runs a shell and tells the shell to run the command you supplied. Then the shell exits. So running an alias command with os.system can basically accomplish nothing useful.
Here's an example of how you might adjust your bash configuration to define an alias persistently:
with open(expanduser("~/.bashrc"), "at") as bashrc:
"# Added by myprogram on somedate\n"
"alias cdd='cd ~/Desktop/'\n"