In Polish names end in

-ski

See in Russian and Belarussian the standard endings for adjectives are long, like doubled:

новый
новая
новое
новые

In Ukrainian you can write them long, but the standard form is short, but the long form is retained in the masculine:

новий
нова
нове
нові

In the other slavonic languages they have short endings:

E.g. in Serbian, the adjective Serbian is Српски, Српска

In Polish the names end in
-ski or -ska (m/f).

Thus Mr. Kaczyński is married to Mrs. Kaczyńska.

But when Polish names are transliterated into Russian, they Russify them to:

Качиньский , Качинськая. If you see something written about the Polish president, Lech Kaczyński, in a Russian newspaper they'll put -ский at the end even though in Polish it ends -ski. (Лех Качиньский)

This means the names will decline:

Дом Качиньского - Mr. Kaczyński's house

Of course in Polish the name would decline in the same way:

Dom Kaczyńskego