This is a noteworthy question and has also been asked elsewhere. The answer is mentioned in the Chaitanya Charitamrita too and is as follows -
In the Chaitanya Charitamrita, Adi Lila, 3rd chapter, purport to the 34th verse, Lord Chaitanya's sannyasa initiation is described as follows:
"During the time of Lord Chaitanya, the influence of Shankaracarya in society was very strong. People thought that one could accept sannyasa only in the disciplic succession of Shankaracarya. Lord Chaitanya could have performed His missionary activities as a householder, but He found householder life an obstruction to His mission. Therefore He decided to accept the renounced order, sannyasa. Since His acceptance of sannyasa was also designed to attract public attention, Lord Chaitanya, not wishing to disturb the social convention, took the renounced order of life from a sannyasi in the disciplic succession of Shankaracarya, although sannyasa was also sanctioned in the Vaishnava sampradayas.
... Lord Chaitanya accepted sannyasa from Keshava Bharati. When He first approached Kesava Bharati, He was accepted as a brahmacari with the name Sri Krishna Chaitanya Brahmacari. After He took sannyasa, He preferred to keep the name Krishna Chaitanya.
The great authorities in the disciplic succession had not offered to explain why Lord Chaitanya refused to take the name Bharati after He took sannyasa from a Bharati, until Srila Bhaktisiddhanta Sarasvati Gosvami Maharaja volunteered the explanation that because a sannyasi in the Shankara-sampradaya thinks that he has become the Supreme, Lord Chaitanya, wanting to avoid such a misconception, kept the name Sri Krishna Chaitanya, placing Himself as an eternal servitor. A brahmacari is supposed to serve the spiritual master; therefore He did not negate that relationship of servitude to His spiritual master. Accepting such a position is favorable for the relationship between the disciple and the spiritual master."
Also, it is noteworthy that Krishna Chaitanya took initiation from Keshava Bharati because although Keshava Bharati belonged to Sankaracarya sampradaya, he was also a great devotee of Krishna. According to some authoritative opinions, although Keshava Bharati belonged to the Sankara-sampradaya, he had formerly been initiated by a great Vaishnava, Srila Madhavendra Puri, see here
Also, regarding the point of guru droha, it is to be noted that Krishna Chaitanya said that his guru himself asked him to always chant the names of Krishna, and that this was the essence of all Vedic hymns (source)