Is there any relation between this name and names such as "Adeodatus," "Deusdedit," etc? This name means "divine gift" and those mean "given by God," so it seems possible.It seems to me that "dare," the Latin infinitive "to give," may have lent a hand in this name, since "gift" is related to "give," and "dar" looks an awful lot like "dare."
Boško is another diminutive of Božidar or, indeed, of any name beginning with "bozy" or "bog". Used in Croatia, Serbia, Slovenia and Macedonia. [noted -ed]
https://hsb.wiktionary.org/wiki/Bo%C5%BEidar [noted -ed]