Not retaining the color in the formatting, when pasting into InDesign

If you're working with black text ... (?) you can also check your 'Appearance of Black' (Preferences). If it is set to 'Output all Blacks as Rich Black', that will cause black text (100% K) to become rich black when exported.  (So choose 'Output all blacks accurately'.)

Do you have a swatch of the same name in the document?
It might be using the swatch you already have in your document.

Can you try change the setting in your preferences
The bottom one here
See if toggling this option makes any difference