Srimath Vedantha Desikar is a Guru of Vaishnavites (Aacharyan) - especially the Vadakalai sect.
Sorry your question mixing the film of that ill-famous womanizer Malahasan somewhat hurts. Any way since you have asked the question, I am bound to answer.
First let us know about Vedanta Desikar here:
Vedanta Desika (1268–1369 CE),
born as Venkatanatha, was a prominent South Indian polymath, philosopher, and foundational Sri Vaishnava guru of the Vishishtadvaita tradition
. He authored extensive works in Sanskrit, Tamil, Manipravalam, and Prakrit, and is regarded as a key leader of the Vadakalai subsect.
Are there Mutts in the name of Vedantha Desikar in South India?
Yes, major monastic institutions rooted in the lineage of Sri Vedanta Desika exist in South India, most notably the Parakaala Mutt, which was founded by his direct disciple. Parakala.
Key Institutions and Centers If you'd like, I can provide: Specific addresses for the branches in Mysuru, Bengaluru, or Chennai
Sri Brahmatantra Swatantra Parakala Swami Mutt (Parakala Matha): Founded around 1338 CE by Sri Periya Brahmatantra Swatantra Jeeyar, a chief disciple of Swami Vedanta Desika. Its historical headquarters are located in Mysuru, Karnataka, with key branches in Bengaluru (Karnataka), Srirangam and Kanchipuram (Tamil Nadu), and Hyderabad (Telangana).
The biggest Parakala Mutt at Mysore - one thousand years old - they say!
Swami Vedanta Desikan Thirumaligai (Srirangam): A historic center and dwelling place associated with Swami Vedanta Desika located in Srirangam, Tamil Nadu.
Thoopul Desikan Sannidhi Mutt: Located in Kanchipuram, Tamil Nadu, marking the birthplace and sacred ground linked to Vedanta Desika's tradition.
Normally in all Vishnu Temples, there will be a “Sannadhi” - place of worship for Desikar. Mostly Temples, which follow “Vadakalai Sampradhaya” will surely have it.
Talking of Vedanta Desikar, there is a Varadharajar temple at Sathyagala, near Kollegal, Karnataka - where Swami Desikan stayed for 12 years and immersed in “Penance”. There is a separate Sannadhi for Desikar with “Nithya Poojas” being conducted.
Every year the Birth Star (Thirunatchathram) festival is celebrated in this small, but very peaceful temple - where you can sit and “pray” the Almighty with Peace - one-to-one!
Vadakalai Vaishnavites end their daily Pooja rituals with a stanza ending “Vedantha Desikaney - Innum Ore Noortaandirum! (Live for one more century) !
Photos courtesy: online sites