:::::Tirkic is not essential and does not need to be mentioned at all. It is not natural to occur in the lead. I repeat for I don't-know-how-many times that we don't say Slavic Bulgarians in any lead. 
 :::::Reasons for not including the Danube Bulgar Khanate (and putting it in a footnote as Constantine suggested): 
 ::::::1. Does not apply for the whole existence of the state 
 ::::::2. It is completely out of context there - it is used to differentiate it from Volga Bulgaria 
 ::::::3. Not the only name used for that period - also we use Danube Bulgaria, Bulgarian Khanate and others 
 :::::PS: I am not going to be home until Monday, so don't modify the article itself until I return to resolve the last details.