As said in other comments -sen names are Scandinavian patronymics used in Denmark and Norway (whereas Sweden mainly uses the -son variant). So yes, it's likely you have an paternal ancestor in Denmark or Norway whose first name was Ebbe.

The system of patronymics involved people taking their fathers name and adding -sen/-sen or -datter/-dotter. Niels Ebbesen was son of Ebbe Strangesen. and if he had a son (Dansk Biografisk Lexikon mentions none) his son was not named Ebbesen. Danes did not abandon traditional patronymics and start inheriting patronymic surnames until the late 18th century at the earliest. (and Icelanders never did) Coming from a noble family, albeit a family of lower nobility about which little is known, Ebbesen's family (if they were still around by that point) would not have used patronymics of any kind after 1526 when Danish nobles were forced by law to adopt non-patronymic house names, after which point only commoners had patronymic names.

So you can't be a descendant of Niels Ebbesen. First since he didn't have any known heirs. Second because even if he did, they'd be named Nielsen and not Ebbesen. And third, by the 1500s they'd be named neither of those things. You could be indirectly related to him through some coincidence but the surname would have nothing to do with it,and the same goes for the 1,889 other people in Denmark and 338 in Norway and 35 in Sweden named Ebbesen.

Tracing your lineage back means you've found a birth record or similar showing who your parents were, and who their parents were and so on. You can trace your lineage back as long as you have an unbroken chain of those. Googling your last name is not tracing anything.

People from r/Genealogy might also be able to help you with this

There's always more to be said about DNA, but regarding last names, it's difficult to make a claim between a last name and ancestry. Although this answer is about Ellis Island and name changes, it gets at part of your question.