Dimension names are of course different form the values held against each dimension, in most cases those values come from system tables, and that would imply that everyone entering data and creating new values would be bi-lingual and would remember to create both values and would do so accurately., nd that a field to hold multiple, translations for each data value would exist.
As far as I know for financial dimensions you can pick up translations of the main account values and also for custom dimension values. You only can enter translation text when < Custom dimension > is selected in the Use values from field in the Financial dimensions form. Normally access control to this would be restricted to finance and not for those who e.g. create items, or projects
Some system fields e.g. item description can hold multi language against the field.
This post will give you an idea of how to extract translations for a custom dimension : https://community.dynamics.com/ax/b/yasirsmicrosoftdynamicsaxworkshop/archive/2017/12/06/translation-text-of-custom-financial-dimension