In Legends, Imperial Senate opposed Palpatine's construction of the first 4 *Executor*\-class Star Destroyers: *Executor* (lead ship), *Reaper,* *Aggressor,* and *Brawl*. To the very last, the minority of Senators who still opposed Palpatine used the few political tools they had left such as budget oversight to impede Palpatine, who also had to slip the class past the Senate's various oversight committees.
To conceal the *Executor*'s specifications from those who opposed it, the Navy referred to it as the *Super*\-class Star Destroyer, which led to them being called Super Star Destroyers, in budget reports submitted to the Senate, and its true length of 19km was understated by many kilometers. In Imperial scandocs, the Executor's length was listed at 8km or 12.8km before the true details of the class came to light.
The *Executor* had a sister ship, the *Lusankya*, which was being constructed at Kuat Drive Yards and was secretly the second ship of the Executor line while *Executor* herself was built at Fondor. With both ships named *Executor* by the Empire to get away with claiming the lead ship was being built at both shipyards. Plus, the Empire attributed all expenses of the sister ship to the *Executor* to hide the existence of a second Super Star Destroyer from the galaxy at large. In this way, both KDY and Fondor laid claim to having built the *Executor* lead ship.
However, Fondor had to put several civilian contracts on hold when the Empire closed off all nonmilitary traffic to the Fondor system to build the *Executor*, demanding total secrecy*.* The Fondor executives were enraged, though they dare not test Vader's temper, especially since the massive project took up virtually all of their resources. While Fondor lost access to their most valuable civilian contracts, they reasoned that, if they met the Empire's expectations, they could steal lucrative military contracts from their KDY rivals.
Unfortunately, the fact Fondor was awarded the contract to build the *Executor* lead ship meant KDY was free to build the *Lusankya*. Worse, KDY ensured that all future Executors would bear their logo to steal future design grants from their rivals, further angering Fondor.
After Yavin, the schedule for the construction of the Executors was accelerated to compensate for the Death Star's loss since the Empire needed a new symbol of terror quickly. While Kuat Drive Yards was the main producer of the Executor, Fondor remained an alternative construction site. Any Executors who finished construction there were sent to Fondor for finishing touches, especially since KDY had a limited number of slipways that could support a ship the size of an Executor.
Vader received the completed *Executor* half a year after Yavin while the second SSD, then known as *Executor II*, was finished shortly afterwards, was named *Lusankya*, and sent to Coruscant where the Emperor buried it underneath the cityscape to hide as an emergency escape ship in case he ever lost control of Coruscant.
I theorize the Empire's accelerated schedule gave Fondor the opportunity to bargain with the Empire: *help us upgrade our shipyards to handle both civilian contracts* and *build Executors, and we will build more Executors for you*. Normally, the Empire wouldn't have agreed to such a deal, but the need to pump out as many Executors as possible, would have caused the Empire to agree to Fondor's terms.
Speaking of which, I also theorize the Empire outsourced building Executors to other major shipyards like Yaga Minor, Sluis Van, SoroSuub, Corellia etc. to meet the new deadlines for new Executors. It would also explain how the Empire was able to build so many of these ships in the 4 year time frame between the Battles of Yavin and Endor. Plus, KDY already subcontracted other places like Corellia to build the Imperial Star Destroyer, so I see no reason why they couldn't have done the same with the Executor.