Many Finnish names have international roots. Some centuries ago Finns used to have official names that were written (usually) the Swedish way (written down by Swedish-speaking officials who did not speak any Finnish; Finland was an Eastern territory of Sweden), but they were not used in everyday lives - people couldn't pronounce those names and therefore most people had nicknames that were based on their official names. By time those nicknames became long-running Finnish first names.
Kaisa is one of them: it is a Finnish variant of Katarina, just like other Finnish female names Kati, Kata, Riina and Kaija. Just like Finnish female names Elli and Elisa are versions of Elizabeth. My name, Silja, is a Finnish version of Cecilia. Male example of this category of names is Matti. It is a Finnish version of Mathias, like Ville is a version of Wilhelm, Kalle a version of Carl and so on.
This category covers most of the Finnish names, so they have the same background as many European names: Biblical/Greek/Latin origins with corresponding meanings. However, there are couple of other categories as well.
There was also a trend of names that have roots in descriptive names, especially in 19th and early 20th century. Like Voitto (victory), Siviä (chastity), Urho (hero), Hilja (quiet), Veli (brother), Sisko (sister), Tyyne (calm). You can probably guess the genders of those names. Most of them sound very "old-fashioned" nowadays.
Then there are the mythological names, like Väinö, Aino, Kalevi, Annikki, Ukko etc. that come from old deities and mythological characters.
There is also a new trend of several decades to give children more nature related names, like Pyry (fierce snowing), Lumi (snow), Pilvi (cloud), Hilla (cloudberry), Vilja (grain), Tuuli (wind), Helmi (pearl) etc. Another trend is to give an international version of a name and not the Finnish version, for example Julia instead of Juuli(a) and Alex instead of Aleksi. The third trend is that of reusing names from about 100 years ago, which seems to be the natural cycle of reusing names (at least in Finland); here basically no one wants to give their child a name that has connotations with their own parents' generation, they sound old and tired. Their grandparents' generation, however, have names that sound fresh again.
A sidenote: in Finland, the first names that run in the family from generation to generation are somewhat common, but they are usually the second or third names; in Finland most people have two or three first names. It is very rare to find a "jr." with the same first name as their parent in Finland. If you have, for example, a run-in-the-family first name "Annikki", you may have a person with first names Aila Annikki, with a daughter named Tiina Annikki, and a granddaughter named Hilla Annikki. Also usually only one child gets this "family first name" (based on people I know it tends to be the eldest child with the approppriate gender who inherits the run-in-the-family first name), so Hilla Annikki's sister wouldn't have Annikki as a second name.
Second sidenote: in Finland basically every first name is gendered and traditionally there are no gender-neutral names. Now the trend of new nature-based names without a long history as a first name has been an opportunity for people who want to have or give gender-neutral names.