In any case, the wife of virATa, the wife of bali, and the masculine forms which named the sons of kRSNa and asamaMjas were all spelt with the unaspirated voiced dental -d- in Sanskrit, i.e., it is feminine sudeSNA and masculine sudeSNa in the Harvard-Kyoto transliteration of Sanskrit spellings. The word sudhA has the aspirated dental -dh- and the two words are not related.
The prefix su- in Sanskrit like the Greek Eu- means good. The root dA (cognate with the root of the word 'dative', for example) means to give. The word deSNA is an old (Rigvedic) formation from that which means 'someone who gives'. It is common as the last part of a compound. Thus, sudeSNA means someone who gives well, propitious, etc.
The word sudhA is derived from the same su-, but the second part comes from dhe meaning to suck (with obvious cognates in Greek and Latin, in the latter case this initial dh- corresponds to f-). From this sudhA came to mean a good drink. amRta comes from the privative a- followed by the past-participle of mR, to die, cognate with the root of English murder. It means that which avoids death. These are unrelated words. There is no sudheSNA in Sanskrit that I have come across.