( The LL in this name is pronounced like 'll' in 'pulling'. The RI is pronounced like 'ri'in 'rib'. )
KOLLAGIRI is the name of the one of the provinces of ancient India. given the sequence of places mentioned along with this in Ashamedha parva, it seems that this name corresponds to present Kollaapuri ( Only a guess! ).
As was the custom in Samskritham, country names are given by the people that inhabited it and the name is always in plural.
The king of a country derives his name by the country he ruled. E.g. Paanchaala is the ruler of the country Panchaalam,
Chaidya is the ruler of the country Chedi, Maagadha was the ruler of the country Magadha etc. The word Kollagiris refers to the land of Kollagiri as well as its people too.
Ashvamesha parva mentions a battle of Kollagiri rulers with Arjuna in the Ashvamedha expedition.
"After praying to Naaraayana, Nara, Sarasvathi and Vyaasa, then one should read the Jayam."
DEDICATED TO MY DEAR NIECE VYSHNAVI KRISHNA