Whentrans_default_domain is used with an expression, the result of the expression is cached into a variable and this variable is stored in theScope to be used for each following usage of the|trans filter.

This var name doesn't need to be random:

• there is only 1 value in the scope, more than 1 variable at a time is never necessary.
• iftrans_default_domain is called a second time, the same variable can be reassigned.

The only benefit of using a random var name would be to prevent usage in the template. The name__internal_trans_default_domain self-explains that it is not meant to be used.