Drupal: User personalization of Taxonomy terms
This sounds like a rather tricky to do.

i18n_taxonomy.module needs to do a lot of hacking and overriding of the taxonomy.module behaviors to always display translated terms. I don't think something like this already exists as a ready to use module.

One option might be to do this using fake translations and building a custom UI which would allow users to create a new personal language and "translate" the terms. However, it won't be able to deal with the merging part. It's also rather hackish...

Another option might be to ditch taxonomy.module completely using either a simple list field (which supports using a callback function for the possible values, but only through the API, see list_field_info()) and then build a UI which allows users to override the default values (and store them somewhere) or maybe even provide custom field widgets and formatters. Depending on your exact requirements, it might be easier to re-implement the features from taxonomy.module you need rather than trying to bend it to your will.