There are some theories suggesting that the first Polish ruling dynasty, Piast is related to Vikings. These theories are not that strong as the hypothesis that Vikings were instrumental in creating the first Russian statehood so that the name rus is of Viking origin. In the present time, the hypothesis whether the first Piast ruler had Viking blood in his vein cannot be proved or disproved but nobody argues the fact, that the relationships between the first Piasts and Vikings were close and very friendly.
Dagome Index, is the first known document, written around 991, which relates to Poland. Mieszko I, read the article about him entitled January 1st - Namesday of Mieszko - Founder of the First Polish Royal Dynasty, is addressed as Dagome or Dago which is a Scandinavian name. There was also a theory, especially spread out by German historiographers that Mieszko name originates from bear (in Polish mieszko or mis) which in reality is of Scandinavian origin and a common Scandinavian name Bjorn. The Polish historians are still not sure about Mieszko's mother, she could be of Viking origin but Mieszko's paternal line is almost certainly of Slavic origin, with the father and grandfather known by Slavic names: Ziemomysl and Siemowit respectively.
The blood of Piasts and Viking rulers were mixed especially thanks to Świętosława, Mieszko Ist daughter. Swietoslawa in a direct translation means "famous for its holiness", but she was not that holy as her first name would suggest!
Swietoslawa and Olaf
Below is Swietoslawa fascinating story:
Swietoslawa (967-1014), known in Scandinavian sagas as Sigrid the Haughty, Gunhilda, Sigrid Storrada (meaning proud), was Mieszko's I daughter and the sister of the first Polish king Boleslav the Brave. Their mother was probably the Christian wife of Mieszko I, Czech's princess, Dobrawa.
Swietoslawa first became a wife of king Eric VI of Sweden in 980 (or 985), she might give a birth to Olof Skotkonung who later became king of Sweden, but this is not completely proven, she became a widow soon.
Swietoslawa became one of the most famous heroes of the Viking sagas but not always in a positive light. She felt in love with the ruler of Norway - Olaf Tryggvason, but he ignored her, therefore he had to pay with his life. According to the sagas her intrigues led to the creation of the anti-Norwegian coalition of seven kings - Dutch, Swedish and Slavic. In the sea battle of Svolder Olaf's Tryggvason 100 ships got defeated by a united fleet of Sweden and Denmark under Olof Skottkonung and Svein Forkbeard and he died heroically there. Sagas tell that this was not the only man, she felt in love with. She ordered to burn alive two others who ignored her feelings.
After 994 she married Sweyn I of Denmark under the name Gunhilda. From the second marriage she probably had five children, including Canute the Great and Harold II of Denmark. Since her marriage was not happy, she returned to Poland where her brother Boleslaw the Brave was ruling. After Sweyn died her sons, Kanut and Karald took her back from Poland. Kanut, known as Kanut the Great became later king of England, Denmark and Norway and governor of Schleswig and Pomerania. She died somewhere in Englisg castle. In any event, Boleslaus I of Poland, the first king of Poland actually sent his troops to help Canute in his successful conquest of England, another sign of close relationships between Polish rulers and Vikings.
It is said that Świętosława's difficult character was inherited after her aunt Adelaide (Polish Adelajda) who was probably a sister of Mieszko I and also the wife of the Hungarian duke Geza. Adelaide became a mother of St. Stephen the Great (977-1038), who became the first king of Hungary and a saint.
Adelaide was known as a beauty, but she drunk excessively and loved riding horses like a man. Once, she even killed a man in a rage.
I recommend this book about Polish history written by Adam Zamoyski and entitled: The Polish Way: A Thousand-Year History of the Poles and Their Culture
I also recommend Polish First Names Author: Knab, Sophie Hodorowicz