What makes "100 lugu matkateelt" more of name in such case? I'd rather say that these are a title and a subtitle. Then alternatively they could be also combined as board:title value "100 lugu matkateelt. 1931 – Sagadi metskonnast sai üks esimesest neljast katsemetskonnast".  Or maybe strapline=* could be used for the shorter title, or some other tag could be introduced for it.

Generally, an information board describes some subject that exists independent of the board. The fact that a board carries a name of a nearby object (or some other text) does not necessarily make this name also into a name of a board. This is similar to street signs or city limit signs that also carry a name but only to denote a location of a different named object.