Is there a way in .bash_profile, to create two aliases that do the same thing?

In short, is there something like this?

alias code,programming='cd /path/to/Programming/; clear; pwd; ls'

Yes, brace expansion:

alias {code,programming}='cd /path/to/Programming/; clear; pwd; ls'

You can only provide one name per body, but you can define one name to be an alias to the other in the same command. For example,

alias code='cd /path/to/Programming/; clear; pwd; ls' programming=code

In practice, I recommend defining a function instead of an alias for the "real" one.

code () {
  cd /path/to/Programming
  clear
  pwd
  ls
}

alias programming=code

On an unrelated tangent, zsh does allow defining multiple names for a single function:

code programming () {
  cd /path/to/Programming
  clear
  pwd
  ls
}

You can do this:

alias foo='ls'   # Arbitrary command. I've used ls for example
alias bar='foo'  # Use alias from previous definition

This can be also one line:

alias foo='ls' bar='foo'

For more info type help alias in your shell.

Btw, I would put these aliases into .bashrc rather than .bash_profile: https://www.gnu.org/software/bash/manual/html_node/Bash-Startup-Files.html#Bash-Startup-Files

You could use

alias code='cd /path/to/Programming/; clear; pwd; ls'
alias programming='code'

or even multiple assignments in a single alias statement, see chepner's answer.

When expanding an alias, the first word is checked for being an alias again, so you can "chain" them, see the manual:

The first word of the replacement text is tested for aliases, but a word that is identical to an alias being expanded is not expanded a second time.

This allows for aliases like

alias ls='ls -F'

without infinite recursion.