You can use either 'a well known actress' or 'the well known actress' after 'Kate'. The difference is the normal one between using an indefinite or definite noun phrase: if you think your reader can identify which well known actress you're talking about, you probably want to use the definite noun phrase. Note that giving a first name is not necessarily enough information for the reader to clearly identify which actress you're talking about. Even if I give both first and last name, my use of an indefinite or definite noun phrase will generally be chosen by whether I think my readers can identify who I am taking about.
For example, if I say
Kate Winslet, the well-known actress, has gone to Italy.
I probably expect that my readers can identify who Kate Winslet is. That is, I think they know who she is.
Another possibility is that, yes, by using the definite noun phrase, I am including my readers among the group of people who know who Kate Winslet is–even if this is not necessarily the case. Perhaps I will further inform them in the next sentences. Or perhaps that's all the identification I choose to make.
If I write
Kate Winslet, a well-known actress, has gone to Italy.
it is probably the case that I don't think my audience (my readers) can identify who Kate Winslet is, beyond the fact that she is well known as an actress to me or to other people, but not to my readers.
My audience here could be people who have no knowledge of any actresses. Perhaps I'm writing to people in the the Amazon who have never heard of movies or actresses.
(Excursis: The use of definite noun phrases and indefinite noun phrases can be very subtle, and they give a writer tools to create with. They don't always follow some easy or binary meaning that learners think or hope they do–language is not logic. The best way is to try to grasp the fundamental usage of definite and indefinite noun phrases and expect them to be used in many subtle ways that will take you a long time to master–that's just the way it is.)