Ok technically if "there are special reasons" they can make an exception, but the default is still that it's forbidden.

When I read comments like these, I just have to look them up. It's something that could very well be true and equally, you could be messing with us. Why would they have such a law? What prompted it to be drafted and accepted? So I did a search on the internet and here is what I found.

I don't know Finish so I cannot read up on their law but according to Info Finland (operated by KEHA Centre if their © is to be believed), this article dated to 19.12.2024 states under the header "Child’s name":

Finland has a law on names. According to the law, everyone must have a last name and 1–4 first names. The first names must be compliant with Finnish law. For example, siblings may not be given the same first name.

Maybe people living in Finland know exactly what KEHA Centre is but I don't so I have to look them up. There are two articles on Wikipedia, one in Finish and one in French. The French one has the title "KEHA Centre" while the other one is titled "Centre KEHA". Translating the articles with Firefox's built in translater, it says (in French) "The KEHA Centre is a national agency providing..." and (in Finish) "Keha Centre [...] is a Finnish government agency that supports employment, integration, digitalisation and knowledge".

According to Sumoi.fi, an alternate name for KEHA Centre is "Employment, Development and Administration Centre". (And what is Sumoi.fi? According to them, "The service is being developed by the Digital and Population Data Services Agency", that sounds official.)

Given the evidence I have found, it looks like Info Finland is a legit website and it looks like it is indeed true that your children cannot have the same first name.