Can this be customized? Of course! That is, if you have a security role with customization privileges. And it's pretty straight forward too.
Here's what the out of the box sales process looks like in a Leads record:
To make changes to this, go to Settings >> Customizations >> Customize the System >> Processes:
The Process we are looking to change is called Leads to Opportunity Sales Process. We could change it directly, but I'd like to keep this around just in case, so let's deactivate it:
Now, let's create a new Process to use in Leads. We'll call it My Company Lead to Opp Process:
After you click OK, another screen will open. Here's where you can add your customizations:
You can enter your own Stage Name, in this case I've called the first stage INITIAL CONTACT. Now you can add the steps associated with this stage. My first step is to get a person's name. I select Last Name as the corresponding field, that is, this step is complete when a last name is entered for the lead. Check the required box if you don't want to allow users to skip this step.
When you're finished defining your Process, you can assign Security Roles to it.
This allows different groups to use different Sales Processes. Handy. Now Save, Publish, and you're all set!