I've wanted to write some more advice posts, and lately I've been thinking about how first and last names are paired together. I know that sometimes absolutely no thought whatsoever is put into choosing the right first name for your baby that pairs well with your surname, (and these names tend to be comical, whether intended or not), but I dare say most parents, even if subconsciously, choose a given name that doesn't seem insanely out of place with their surname. There will always be John Wu, Angel Black, Kimantha Stanislav, and the like, where the two really don't seem to fit, but there are ever more names that just seem right together, such as Bill Clinton, Colin Firth, January Jones or Jennifer Anniston, as far as celebrity examples go.
My advice is to take your surname into heavy consideration before choosing a given name. Think about what it means, what the name conveys, what culture it honors, what kind of image it brings to mind.
However, my question, as I've seen asked dozens of times, is can you pair a given name that is obviously from a particular culture or country, with a surname that is obviously from a very different culture or country? I imagine something like Siobhan Smith or James Takeuchi. It might be easier to say "Of course you can" when the names sound excellent together, as Siobhan Smith does, or if you have a connection to both cultures/countries (for example, your surname is French, you come from France, but your significant other is from Japan, and you'd like to honor both). And of course, just because a name originated in Greece or Italy or wherever, doesn't mean it's destined to only be thought of as Greek, Italian or whatever. A lot of those names are now simply thought of as "American." Jessica comes to mind.
In my personal opinion, I think it is a lovely idea, and no one ever said you can't do it, as long as you consider everything seriously. No matter what your surname, no matter what given name you're thinking about using, it's always a good idea to ask yourself (and others) whether the names sound good together, what impression the child's name might make, if the meanings or assumed cultures conflict, etc. It might just be a little bit weird to be named Parvati Jameson or Guadalupe Chan, but a little Fionnuala Fischer or Anastasia Sanderson might be cute.