Detect named entities inside words
I would recommend to look into character level named entity recognition. For example: Kuru et al, CharNER: Character-Level Named Entity Recognition, Proceedings of COLING 2016, the 26th International Conference on Computational Linguistics: Technical Papers (2016) 

The authors evaluate on many highly inflected languages including Turkish, so this should be adequate for your Finnish use case

The code is here: https://github.com/ozanarkancan/char-ner

You should hopefully be able to download and get it running out of the box for training. Of course I am assuming you have a tagged NER corpus in Finnish, which you would need to preprocess to get into the same format as the CSV file that they use for Czech in the repo.