Ever wondered how Rajaraja chola's Shiva ended up being called Brihaddeeswara? When he built it, apparently, he just called the temple as Periya kovil, which is infact what the locals refer to it till date - the Tanjai Periya Koil.
The cholas didn't have the practice of building separate shrines for Parvati, and Rajaraja chola was no exception. When completed in the 11th century, the Big temple was a collossal structure, but it didn't have the shrine of his consort. Incidentally, even during the chola reign from 1000 AD till 13th century, Madurai was ruled by the chola vassal kings who carried the surnames chola pandian! Post the demise of Rajaraja Chola, there was a revival in the Pandian dynasty. The revived Pandian kings took back not only Madurai, but also the chola headquarters of Tanjore along with the chola kingdom.
And in the brief period they ruled that lasted less than 150 years, one of the pandian king built the shrine for Parvati right in the temple complex and the goddess consecrated there was called Ulagamuludaiya naachiyar. The 150 year of pandian rule started with son of Vikrama pandian, jatavarman kulasekara pandian 1 (who ruled from 1190 AD till 1210 AD) and went on till Vira Pandyan IV (1309 to 1345).
Now around this time there was a war amongst the pandyans as to who'd succeed and that caught the attention of Malik Kafur who invaded the south and started his attack on Tanjore. The powerful vijayanagara empire thwarted the attempts of Malik Kafur and brought Tanjore and Madurai under them. Madurai and the whole pandya and chola kindgom including tanjore was ruled by the tax paying nayaks who reported to the vijayanagar kingdom for a while.
The goddess Ulagamuludaiya naachiyar was called in sanskritized version as Brihannayaki - or the big goddess as she presided over the big temple. And duly lord Shiva was was earlier called Peruvudaiyar was also sanskritized to go with his consort's name as Brihadeeshwara, almost 2 centuries post he was consecrated. This happened thanks to the addition to the temple by the nayaks or the vijayanagara empire.
It was the Pandyan kings who's lost in history rule of 150 years that gave the goddess shrine in Tanjore. Finally, it was the Vijayanagara empire that anointed the name Brihannayaki that led to subsequent name change for shiva from Peruvudaiyar to Brihadeeshwara...
That made way for Rajarajeswaram to be called as Brihadeeshwaram....