Facts first: Nõmme Kalju... Nõmme is one of the 8 districts of Tallinn & Kalju means Cliff or rock. So Location-clubs name. And they were JK Nõmme Kalju before the club owner decided that they should use international FC.

JK Sillamäe Kalev... Sillamäe is a town in north-east Estonia. Kalev is a nationwide sports sssociation. Again Location and name.

Belive me in Estonian language attributive adjective comes before the object and most of the clubs have place name in front. 

Your other arguments arr all WP:OSE. Nobody calls it Tammeka Tartu in Estonia. As I said You can find this wrong version, because some people decided to create some unified system for names which was wrong. You shouldn't cherry pick sources. Estonian FA is the main source. Others can make mistakes.. for example just two weeks ago BBC used first names as family names for Levadia players in thir Champions league match review Levadia vs Crusaders F.C.  

Nõmme Kalju and Sillamäe Kalev have played in 2015–16 UEFA Europa League they were not called Kalju Nõmme And Kalev Sillaäme