Well, "nen" ending clearly means "a" thing, like just one thing. For example "Aaltonen" = a wave. But "Aalto" = wave (in general). Great players like Kurri, Selänne, Laine have been general versions of the word
All those three names also cant be bent using the "nen" ending, they're exceptions.
"Lainen" endings clearly means like "member of", perhaps many times a family but some times some nature thing. But the Lainen ending clearly means "member of" some kind of group.
-nen is multi-purpose noun in Finnish language, and it's interesting topic for discussion as nearly always some context of use will be missing...
[collapse=nennouns]
-nen nouns
(following Wikipedia:
https://en.wikipedia.org/wiki/Finnish_grammar)
This is a very large class of words which includes common nouns (for example 'nainen' = 'woman'), many proper names, and many common adjectives. Adding -nen to a noun is a very productive mechanism for creating adjectives ('muovi' = 'plastic' -> 'muovinen' = 'made of plastic'/'plastic-like' ). It can also function as a diminutive ending.
The form behaves like it ended in -s, with the exception of the nominative, where it is -nen. Thus, the stem for these words removes the '-nen' and adds '-s(e)' after which the inflectional ending is added:
Finnish |English
'muovisessa p***yssa' |'in the plastic bag'
'kaksi muovista lelua' |'two plastic toys'
'muoviseen laatikkoon' |'into the plastic box'
Here are some of the diminutive forms that are in use:
Finnish |Stemming from |English
'kätönen' |käsi |'a small hand' (affectionate)
'lintunen' |lintu |'birdie', 'a small bird'
'veikkonen' |veikko |'lad'
'kirjanen' |kirja |'booklet'
'kukkanen' |kukka |'a little flower'
'lapsonen' |lapsi |'a little child'
The diminutive form mostly lives in surnames which are usually ancient words many of whose meaning has been obfuscated. Some of the most common:
Finnish |From word |English
'Rautiainen' |rautio |blacksmith (of a blacksmith's family)
'Korhonen' |korho |'deaf' (of a deaf man's family)
'Leinonen' |leino |'sorrowful, melancholic'; alternatively male name Leino as short for Leonard
'Virtanen', 'Jokinen', 'Järvinen', 'Nieminen'... |virta, joki, järvi, niemi |'the family from by the stream (virta), river (joki), lake (järvi), peninsula (niemi)'
'Mikkonen' ||[A family name assimilated from the name of the farmhouse, after the householder's name 'Mikko']
'Martikainen' ||possible origin Martikka, a South Karelian surname, identical to Russian surname Martika
'Lyytikäinen' ||from 'Lyytikkä', originating to Germanic male name 'Lydecke'
Occasionally such nouns become place-names. For example, there is a peninsula called "Neuvosenniemi" beside a certain lake. "Neuvonen" means "a bit of advice/direction"; at this peninsula people rowing tar barrels across the lake would stop to ask whether the weather conditions would allow to continue to the other side. Most place-names ending with -nen assume a plural form when inflected. For instance, the illative of "Sörnäinen" is "Sörnäisiin" instead of singular "Sörnäiseen".
...
(Also appears as)
Interrogative pronoun
Finnish |English
kumpainen |which (of two) - (old or dialectal word)
Indefinite pronoun
Finnish |English
jokainen |every, everyone
Indefinite adjective
Finnish |English
toinen |(non-reciprocal, non-numeral use) another
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..
An example how -nen can appear a lot in various functions in the Finnish sentences:
"Herra Nenonen on aikamoinen veikkonen. Hänen ensimmäinen vaimonsa on kiinalainen ja toinen on brasilialainen. Alkuperäinen vaimo on niin kateellinen, että hänen naamansa on punainen."
-->
"Mr. Nenonen is quite lad. His first wife is Chinese, and and the other is Brazilian. The original wife is so jealous that Her face is red."
One cannot have much more Finnish name then Laine, without -nen.