Polish writer Jadwiga Łuszczewska (pseudonym Deotyma), 1834–1908, painted by Mateusz Zarzecki ca. 1848–52
Hadewig is an Ancient Germanic name derived from roots hadu (combat, battle) and wig (war). Like many other names of Germanic origin, its meaning relates to war and battle. This is such a striking contrast to how many Slavic names have meanings related to love, peace, glory, dearness, and flowers.
Probably the form most familiar to people is the modern German form Hedwig, which hasn’t charted in Germany for decades. It was in the Top 20 from 1890–97, and again in 1901 and from 1903–08. Needless to say, it’s considered very old-fashioned for a reason!
Other forms of this name include:
1. Hedvig is Scandinavian and Hungarian. The Scandinavian nickname is Hedda, and the Hungarian nickname is Hédi. In 2019, this name was #78 in Sweden and #65 in Norway.
2. Hedviga is Slovak, Slovenian, Latvian, and Croatian.
3. Hedvika is Czech and Slovenian.
4. Hadewych is a rare Dutch name. It was much more common in the Middle Ages. The nickname is Hedy (also used in German).
5. Hedwiga is Czech, Romanian, and Medieval Polish.
6. Hedwige is French.
7. Heiðveig is Faroese. In Icelandic, this is a separate name derived from roots heiðr (honour) and veig (power, strength).
8. Hekewika is a rare Hawaiian form.
9. Heiðvík is Faroese.
10. Hedla is a Silesian–German nickname sometimes used as a full given name.
Hedvig Elisabeth Charlotte of Holstein-Gottorp (1759–1818), Queen of Sweden and Norway, and a prolific diarist
11. Edvige is Italian and Corsican. The nickname is Edda.
12. Edwige is French.
13. Edubige is Basque.
14. Eduvixes is Asturian and Old Galician.
15. Edviga is a rare Moldovan, Romanian, and Portuguese form.
16. Edwikke is East Prussian–German.
17. Edvija is Old Occitan.
18. Eduvigis is Medieval Spanish and Catalan.
19. Edwiga is Medieval Polish.
20. Avoise is Medieval French.
French stage and film actor Edwige Feuillère, 1907–98
21. Jadvyga is Lithuanian.
22. Jadwiga is Polish. I have two characters by this name, one a minor character who goes by Wisia, and the other a main character (in an entirely different set of books) who’s referred to by her full name in the narrative and called Wisia and Jadzia. Other nicknames include Jagusia, Jagienka, Jagna, Jagoda (which also means “berry”), Jaga, and Iga. Both of my Jadwigas were born in the 1920s.
23. Yadviga is Belarusian.
24. Heta is Finnish.
Onomastics Outside the Box 
Indeed, it’s funny how Germanic and Slavic names contrast so much, I’ve only just fully realised because of your post how strong this contrast is even though it’s pretty obvious when you look closely at name meanings.
Hedvig’s very “combative” meaning is why I don’t really have a lot of positive feelings for this name, in any form. Not that I don’t like any names referring to things like war or battle but this one feels a bit too harsh with both all the root words it comes from having to do with it and the sound of it being pretty harsh. It also does feel really dated, although I’ve seen lately a few mums on a Polish baby name forum being interested with Jadwiga and considering using it for their babies, but I can’t think of one who would actually go ahead with the idea. In my personal opinion it could wait a bit longer to feel fresher. Iga on its own has been very well liked though, just like a lot of similar nickname names. And Jagoda’s quite trendy too.
Some of the nicknames of Jadwiga are pretty nice though, like Wisia feels really homey, and I quite like Iga and Jagna as well.