How to override form/register.phtml template in Magento 2?

You can override register.phtml file using layout XML way or directly add template file to theme level by theme module.

register.phtml file used to display a Customer registration form in frontend.

Block name is customer_form_register which contains the register.phtml template.

you can see registration form by URL, <SITE_URL>/customer/account/create

Magento Opensource Template Location:
In Opensource, register.phtml file coming from Magento_Customer module.

Magento Commerce|Cloud Template Location:
In Commerce/Cloud Version, register.phtml file coming from Magento_CustomerCustomAttributes module.

You can override using Layout XML inside a module by <referenceBlock> node inside your customer_account_create.xml file.

Create a XML file, app/code/<Rbj/Modulename>/view/frontend/layout/customer_account_create.xml
In above path, <Rbj/Modulename> replace with your Package/Modulename.

Create a template file at location,
app/code/<Rbj/Modulename>/frontend/templates/form/register.phtml

Clear a cache and check your registration page.