Not only is describing it as "European" far too broad, but I think there is sufficient evidence that the original entry is correct in saying it's from
Alyssa.
It seems like a Modern English (language) name, which, if it had to be in
Europe, would typically put at least the bulk of its usage in Britain, but there's no recorded usage of Analyssa in England & Wales at least.
http://names.darkgreener.com/#analyssa
I also tried the Netherlands since they do occasionally adopt modern English names, nothing:
http://www.meertens.knaw.nl/nvb/naam/is/Analyssa
The only recorded usage I can find of it is in the United States.
http://www.babynamescience.com/baby-name/Analyssa-girl
Its recorded usage in the 1990s coincides with
Alyssa's popularity.
http://www.behindthename.com/name/alyssa/top/united-states
Alyssa peaked in 1999 and continued to be popular in the early 2000s. I think this is decent evidence the entry is correct as it is.
OP,
Annalise,
Annalisa, Anna-Liisa and
Anneliese and variants listed on this site are recorded in European countries, but Analyssa isn't. That's not to say there are no Europeans called Analyssa, but there isn't sufficient evidence to say it's a "very European" name.