Do most cultures have first names that are mostly unique to either males or females? By first name I mean not the family or surname.
I am aware that non western cultures don’t always use names the same we do in the US and Europe.
It’s certainly true in Spanish, and while I don’t know Chinese, I asked a student this question once and he said it was mostly true for Chinese given names.
Pretty much so in Japanese. Many, if not most girls’ names have “ko” at the end, which means “little” with a strong implication of “cute because small”. Many (but not most) boys’ names have characters that mean “male” built into them, especially the unimaginative ones like “first son”. In my limited experience I have only run across one ambiguous name, “Kaoru”, which I gather is mostly for girls but can also be used for boys (not sure if it is the same character in both cases).
In the variuous cultures of Pakistan; yes.
However, names do tend to “migrate” and some have done so recently. And there are unisex names.
True in Hebrew.
True among most Jewish cultures though the centuries. Things male and female are kept discretely separate. I can’t vouch for all of secular modern Israel, though.
True in Slavic cultures too, and in Greek culture. That’s about the limit of what I can vouch for.
Oh, among American Deaf people, name signs and NOT gender specific, but they are more like nicknames than full names. Kinda like “Terry,” which could be short for either Terrence or Theresa.
Regarding Hebrew names: there are a few names which gentiles have pulled out of the scriptures without looking carefully to see what gender they belong to, effectively creating a name that is a boy’s name among Jews, and a girls name among gentiles. A couple of prominent examples are Ariel and Azaria. In Hebrew, the feminine ending for a name is -it, so you have Yehudah (Judah)m. and Yehudit (Judith)f.; Yonah (Jonah)m. and Yonit (sometimes rendered Janet, but Janet has other translations)f.; Shlomo (Solomon)m. and Shulamit (no typical English equivalent)f. There are lots of Hebrew girls names that end is a/ah (Rivkah/Rebecca, Devorah/Deborah, Chava, Leah, Chaya, Hannah) but an -a/-ah ending is no guarantee of a feminine name.
The term you’re looking for is “given name,” as opposed to “family name.”
There are a great many gender neutral first names:
Alex, Brook, Chris, Drew, to name a few. Many are diminutives that have become full names, but I think that it has become harder these days to tell a person’s gender (and never mind those whose gender is not male/female) from their first name.
I used to have an Uncle Hillary and I have a new female niece called Taylor. Is it the case that girls get traditional boy’s names more often than the other way around? I suspect that a boy named Sue would still have problems.
Was that Uncle Hilary or Hillary? One L or two?
As with Francis (male) and Frances (female) spelling often matters.
Hilary has long been a male name. See St Hilary of Poitiers, of the 4th century AD.
What I find interesting is that almost every male name has a female variant, but so far as I know, no female name has a male variant. Thus, for instance, Joan or Jane is a variant of John, Josephine is a variant of Joseph, Patricia is a variant of Patrick, and so on, but there’s no male version of Mary, or Elizabeth, or Rebbecca.
I also find it interesting that, in English at least, there are a number of categories of words that can be female names, like flowers (Rose, Lily, Violet), gems (Ruby, Pearl, Amber), times (Dawn, April, Summer), and virtues (Faith, Hope, Charity), but there are almost no such common male names (the only one I can think of is Victor, and that comes from German which coincidentally has the same word.
In Germany, this was mandated by law until very recently [1]: A given name was supposed to unambiguously identify the gender of a person. A notable exception, mainly in Catholic regions, is Maria, but only in combination with another (male) name. Unlike, for instance, in the US, parents cannot simply make up a new name for their child.
[1] The current legal situation regarding given names is somewhat unclear; actually it is rather confusing.
Many languages have gendered nouns, and given names that are nouns. It might be that *hill *is a masculine noun, so only males are named Hill.
Bolding added - what about “Mario”? Can’t get more manly than Super Mario. 
I find that hilarious.
In Spanish, some masculine nouns are used for female names, which sounds weird to me: Rosario = rosary; Rocio = foggy dew; Pilar = pillar.
This is anecdotal, but a friend of mine comes froma family of Kurdish immigrants and has a name that I’ve seen in both men and women. She told me that in the Kurdish language it is very common to have unisex names, in the sense of the exact same name (not a dimunitive or shortened form of another name) being used for either gender.
It’s true for Hebrew only in classical,biblical Hebrew.
In modern Israeli Hebrew --the opposite is true. Half of the names given to kids in the past couple decades are unisex, and you can’t tell from the name whether its a boy or a girl,.
Wiktionary says that Mario derives from the name of a Roman clan (or gens), Marius, possibly derived from the god Mars. If it’s Roman in original, it likely is completely unrelated to the name Mary, but it does mention that it’s often seen as a masculine form of Maria (and thus Mary) even if it’s not etymologically related.
This used to be the case, but it’s now hopelessly dated.
Women in my generation, their 50s and older certainly had many ko’s but now I only found two in the top 100 girls names, with the highest rank is 39th. There was a period where seemingly all girls’ names ended in an “e” but that fad is also long past.
Likewise, the character for male is not nearly as prevalent.