ΔE 15.8, loose: different enough that you should pick on purpose. Amethyst Rayne is noticeably lighter, warmer than Triumphant Navy.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 16). Amethyst Rayne is noticeably lighter, warmer than Triumphant Navy.
The same difference applies the other way round: Triumphant Navy is noticeably darker, cooler.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See Triumphant Navy on the colour wheel See Amethyst Rayne on the colour wheel
All matches: Triumphant Navy equivalents · Amethyst Rayne equivalents