"Mahadeva", by definition means "The Supreme/Great God". In traditional Hindu mythology, Lord Vishnu and Lord Shiva have an equal standing as Preserver and Destroyer respectively which maintain the cosmic balance. Judging by their roles and standing, I would have assumed that both of them would hold the title and yet when the title is used, it is invariably for Lord Shiva. Is there a reason for why only Lord Shiva is called the Mahadeva and not Lord Vishnu ?
Such a thing is clarified in Karna Parva, in a conversation between Duryodhana and Shalya about the latter being the charioteer of Karna, in the process Duryodhana narrates the destruction of Tripura:
Duryodhana said, 'O supreme among kings! The gods accepted what the lord of the gods had said. 324 All of them gave him half of their energy and he became superior. The god became the strongest among all the strong ones. From that time, Shankara came to be known as Mahadeva.
Krishna Vasudeva while summarizing hierarchy of various manifestation of Shiva, he described Mahadeva as well in Anushashan Parva,
"Vasudeva said, 'O mighty-armed Yudhishthira, listen to me as I recite to thee the many names of Rudra as also the high blessedness of that high-souled one. The Rishis describe Mahadeva as Agni, and Sthanu, and Maheswara; as one-eyed, and three-eyed, of universal form, and Siva or highly auspicious. Brahmanas conversant with the Vedas say that that god has two forms. One of these is terrible, and the other mild and auspicious. Those two forms, again, are subdivided into many forms. That form which is fierce and terrible is regarded as identical with Agni and Lightning and Surya. The other form which is mild and auspicious is identical with Righteousness and water and Chandramas. Then, again, it is said that half his body is fire and half is Soma (or the moon). That form of his which is mild and auspicious is said to be engaged in the practice of the Brahmacharya vow. The other form of his which is supremely terrible is engaged in all operations of destruction in the universe. Because he is great (Mahat) and the Supreme Lord of all (Iswara), therefore he is called Maheswara. And since he burns and oppresses, is keen and fierce, and endued with great energy, and is engaged in eating flesh and blood and marrow, he is said to be Rudra. Since he is the foremost of all the deities, and since his dominion and acquisitions are very extensive, and since he protects the extensive universe, therefore he is called Mahadeva. Since he is of the form or colour of smoke, therefore he is called Dhurjati. Since by all his acts he performs sacrifices for all and seeks the good of every creature, therefore he is called Siva or the auspicious one. Staying above (in the sky) he burns the lives of all creatures and is, besides, fixed in a particular route from which he does not deviate. His emblem, again, is fixed and immovable for all time. He is, for these reasons, called Sthanu. He is also of multiform aspect. He is present, past, and future. He is mobile and immobile. For this he is called Vahurupa (of multiform aspect). The deities called Viswedevas reside in his body. He is, for this, called Viswarupa (of universal form). He is thousand-eyed; or, he is myriad-eyed; or, he has eyes on all sides and on every part of his body, His energy issues through his eyes. There is no end of his eyes. Since he always nourishes all creatures and sports also with them, and since he is their lord or master, therefore he is called Pasupati (the lord of all creatures)...
Having pasted till Vishwaroop form of Shiva there is more to it, read from the page linked to it. One should also note that these names are not mutually exclusive. Any diety can be extolled by any name. (Leave deity, today one particular leader was called Rudra by his fanatics) so one should see the traditions and legacies of names instead of taking figure of speech seriously...
If I may interpret this paragraph philosophically, it is saying the formless Shiva has mainly two forms (how paradoxical!) one is subjective/male another objective/female. All manifestations out of unmanifest is conglomeration of this subjectivity and objectivity with its various powers. Since, one of conglomerate is constantly engaged in the duties of lordship the particular conglomeration is called Mahadeva. Actually, it is very diverse paragraph which is in essence saying everything is Shiva, there is many Shiva out of one Shiva dispersed with many names and powers.
BTW, how surprisingly the essence of this paragraph matches with the one spoken by Lao Tsu...
The Tao begot one.
One begot two.
Two begot three.
And three begot the ten thousand things.
The ten thousand things carry yin and embrace yang.
They achieve harmony by combining these forces.
Ying/Yang is equivalent to Male/Female or Subjective/Objective or Shiva/Shakti...
Why is Lord Shiva identified as Mahadeva?
Mahabharata mentions few reasons for this:
[Devasthana:] Clad in deer-skins, the high-souled Mahadeva, having poured his own self as a libation in the sacrifice called Sarva [SarvaMedha yajna], became the first of gods. ~Mahabharata: Santi Parva: [Rajadharmanusasana Parva:] Chapter 20
[Vyasa:] And since he protecteth this vast universe, he is for that reason called Mahadeva. ~ Mahabharata: Drona Parva: [Drona-vadha Parva:] Section CCII
[Vasudeva:] and since he protects the extensive universe, therefore he is called Mahadeva. ~Mahabharata: Anusasana Parva: Section CLXI
[Duryodhana:] Taking half of their energies from all of them [gods], he became superior in might. Indeed, in might that god became superior to all in the universe. From that time Sankara came to be called Mahadeva. ~Mahabharata: Karna Parva: Section 34
Is there a reason for why only Lord Shiva is called the Mahadeva and not Lord Vishnu?
Lord Vishnu is also called Mahadeva in few versions of Vishnu Sahasranama. For example, Mahadeva appears as 491th name in Vishnu Sahasranama found in Mahabharata: Anusasana Parva:
65 गभस्तिनेमिः सत्त्वस्थः सिंहॊ भूतमहेश्वरः (gabhastinemiḥ sattvasthaḥ siṃho bhūtamaheśvaraḥ)
आदिदेवॊ महादेवॊ देवेशॊ देवभृद गुरुः (ādidevo mahādevo deveśo devabhṛd guruḥ)
Wikipedia: Vishnu Sahasranama also mentions "491 महादेवः mahaadevah" in The Thousand Names of Lord Vishnu section.