How to change a fields label name based on another fields value?
Consider using the Conditional Fields module. Excerpt from its project page:

Conditional Fields allows you to manage sets of dependencies between fields. When a field is “dependent”, it will only be available for editing and displayed if the state of the “dependee” field matches the right condition.
When editing a node (or any other entity type that supports fields, like users and categories), the dependent fields are dynamically modified with the States API.
You can, for example, define a custom “Article teaser&quot; field that is shown only if a &quot;Has teaser&quot; checkbox is checked.

So if you have like 6 possible values (Option 1, ... Option 6), as in your comment below the question, you could create 6 fields with label &quot;Option 1&quot;, ..., &quot;Option 6&quot;.
Not sure if it is acceptable to &quot;split&quot; your &quot;Field Two&quot; in like 6 separated fields, but at least it would change the field labels as you are asking for.