There's no dynamic flags in EU like there is in Hearts of Iron; each tag can only ever have one flag and that flag has to last them the entire length of the game (1309-1865) unless they form a new nation. We at one time tried having nominal formable nations for every single rendition of different flags and it was both cumbersome and bug-ridden (because all flavour events had to consider all possible tags for a country) so the decision was made to select flags that covered the largest period of history and leave it be.
The Ottoman Empire was named after the Osmani dynasty, but other Turkish beyliks in 1309 can still form a united Turkey so that name is more generic in the event some other dynasty forms the united tag. Cores are beneficial to higher revenue, more 'stable' stability (the more core provinces the more it dillutes unrest in a few of them), and higher development growth.