Just thinking through how we might implement such a change, and taking inspiration from other rules:

Option 1

One approach would be to introduce a new array option for alias names to be allowed/ignored by the rule, for example:

{
  "rules": {
    "@typescript-eslint/no-type-alias": ["error", {
      "allowAliases": "never",
      "ignoredTypesNames": ["Record"]  // <- new option
    }]
  }
}

Doing a quick survey of other rules that support an array of things to allow/ignore, there doesn't seem to be a lot of consistency in how these options are named. Some use the prefix "allowed..", some use "ignored..", other use a "..ToIgnore" suffix e.g.

So if we took this approach, is there a preference for what the new option should be called?

Option 2

An alternate approach, which is perhaps not quite as flexible/extensible as the first option, would be a boolean specifically for allowing Record to be used for indexed objects, e.g.

{
  "rules": {
    "@typescript-eslint/no-type-alias": ["error", {
      "allowAliases": "never",
      "allowIndexedObjects": true   // or more explicitly: allowRecord?
    }]
  }
}

This follows the existing pattern of booleans for other types of exceptions to the rule (e.g. allowCallbacks, allowLiterals, allowTupleTypes etc.)

Option 3

A third option would be a new value (or set of values) for the "allowAliases" option, e.g.

{
  "rules": {
    "@typescript-eslint/no-type-alias": ["error", {
      "allowAliases": "in-indexed-objects"
    }]
  }
}

This approach may also require additional values for all composition types, e.g.

type Values =
  | 'always'
  | 'never'
  | 'in-unions'
  | 'in-intersections'
  | 'in-indexed-objects'                                // new
  | 'in-unions-and-intersections'
  | 'in-unions-and-indexed-objects'                     // new
  | 'in-intersections-and-indexed-objects'              // new
  | 'in-unions-and-intersections-and-indexed-objects';  // new

I be happy to have a stab at a PR for this, just looking for a bit of guidance as to which approach best fits with conventions.

I think it's similar as #3181

And the solution at #3181 (comment) could also help.

It runs very well in my projects through https://github.com/1stG/configs/blob/master/packages/eslint-config/overrides.js#L184-L192