Nityananda! Gauranga! Hare Krishna! Good question. Dvapara and Treta are named after the numbers two and three. Satya is named the divine qualities of truthfulness which fully existed in that Kali Yuga. Kali is name after the bad vices of Kali Yuga.
There is a confidential reason for why the cycle of yugas was changed in this Chatur Yuga with Treta Yuga coming before Dvapara Yuga.
The original Lord Krishna, the source of everything, wanted to enact His highest pastimes of Shri Vrindavana Dhaam and He knew that He would not be able to freely distribute this Vraja's love and give entry to everyone into these confidential pastimes as He would be very busy in performing His pastimes and killing the demons to reduce the burden of the earth. So He knew that He will have to come in the form of Lord Gauranga later to freely distribute the love of the pastimes which He had enacted earlier as Lord Krishna. And His advent as Lord Krishna had to be in Dvapara Yuga and as Lord Gauranga had to be in Kali Yuga.
So even though normally Dvapara comes after Satya Yuga and before Treta, He reversed the order of the Yugas and Dvapara now came after Treta and before Kali Yuga. This is because Lord Krishna wanted to distribute His Vrindavana love to all conditioned souls in the form of Lord Gauranga without a big time difference between these two advents of His so that the Vrindavana pastimes are still fresh in the hearts and minds of the people so that when He distributes them as Lord Gauranga, people will accept this love very easily.
If Lord Krishna would have come in the beginning of Dvapara Yuga or if the cycle of Yugas was not changed, the time difference between Lord Krishna's and Lord Gauranga's advent would have been around 1,296,000 years which is the normal duration of Dvapara Yuga plus another 4500 odd years of Kali Yuga. So if in these more than 1 million years, Vrindavana Dhaam would have disappeared, then He would Himself not be able to go to Vraja Dhaam and fulfill the internal purposes of His advent. And the memories of the people of Lord Krishna's pastimes would be very distant if at all existent which would make it difficult for Him to distribute His love of the Vrajavasis.
This is a very confidential secret which even the big Vedic scholars are not aware of because they have no faith in Lord Gauranga Mahaprabhu. But without this understanding, no one can explain why the cycle-order of the Yugas is changed only in the 28th Chatur Yuga on the 7th Manvantara, once in every day of Brahma. This is because Lord Krishna and Lord Gauranga come only during this Chatur Yuga, once in a day of Brahma.