Italian last Name dai history ? Later changed to day?

so I know very few about my family history being my grandparents passed and so I would love to find out more about myself , is there any free sites besides ancestory, that I can look up , my last name is day originally spelled dai until it was Americanized , it is Italian but that’s really all I know , any info would be great, thanks!
Answers

Maxi

Names are nothing to do with 'family history' ALL names are words and all names are chosen. Word history is called etymology and lots of words can be used and come from lots of languages Dai is Welsh langauge and means David, also a masculine Japanese language given name.

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my surname was anglicized to the ENGLISH equivalent

Anonymous: https

https://answers.yahoo.com/question/index?qid=20190118220636AARiMBL