Or is it better to just call it 'first note' (eg: In D Dorian, is 'D' the tonic or just 'first note'). And I suppose same question for the the rest of the scale degrees too (super tonic, mediant etc.). Should these terms only be used for the tonal system when naming degrees of tonal major and minor scales? Thanks.
In any major key, the tonic is the 'base note' - 'home', giving the note's name to the key.
That also works for minor keys - the tonic of key F minor is, of course, F. A sort of datum point from which everything else in that key is measured.
So, using D Dorian as an example, its tonic should be D. Whilst, true, it uses the exact same notes as C major, its 'base note' is D. So that's its tonic. It follows that the other names - mediant, subdominant, etc., follow appropriately.
Calling that root note 'first note' won't hurt, and certainly will be understood - probably by more folk than using 'tonic', 'subdominant' etc..!
Tim's answer is right on, but I wanted to mention one historical issue depending on what genre you mean:
In pre-tonal (that is, modal) music of around the seventeenth century, the term in use would have been "final." Thus in, say, a madrigal in D Dorian, we would refer to D as the "final" and not "tonic." Tonic in this sense came later, so it would be anachronistic to use that term in music written this early.
But if you're talking about modal music written more recently, then yes: feel free to use the term tonic!
In old music it was not the first note but the final note - FINALIS like Richard says - to identify the TONE in which a melody was sung or written.
The following quote is a google translation of this page by U. Kaiser, a German music teacher:
If you have thought that the Lydian mode can be recognized by the tritone f-b and the Dorian mode by the major sixth d-b, you can expand your knowledge in this tutorial. Unfortunately, with regard to music of the 16th century, this way of thinking often leads to an incorrect determination of the key or mode. The so-called characteristic intervals (tritones for Lydian and major sixths for Dorian) can only help to determine the Lydian or Dorian scale or at best the key of a simple composition from the microcosm of Bela Bartók. The following instructions offer practical help in dealing with older polyphonic music and in many cases enable the key or mode of music composed before 1650 to be determined appropriately.
Proceed as follows:
Determine the finalis (the beginning and end of a composition are usually revealing here) Then determine the third above the final, taking into account the general key signature. If the third above the final is minor, determine the second above the final from the general keying. If the second above the finalis is large, the composition is in Doric mode (Doric). If the second above the finalis is small, the composition is in the Phrygian mode (Phrygian). If the third above the final is major, determine the second below the final by using the general key signature. If the second below the finalis is small, the composition is in Lydian mode (Lydian). If the second below the finalis is large, the composition is in Mixolydian mode (Mixolydian).