Normally Mohan is the most common name for Krishna in Gurbani. Other common names include Gobind and Gopal, etc. Reference:: Sikh Philosophy Network http://www.sikhphilosophy.net/questions-and-answers/38559-who-is-mohan.html
Quickly: Kanwaljit ji is correct. Krishna is called Mohan, the seducer, the enticer, when He seduces the Gopis, the village girls. They are fascinated by his dark form
1 and flute
2 and want to be His bride. Krishna's stories have led to a sort of Indian romanticism, where the Bhagat singers relate to Krishna as one of the Gopis, wanting to be his bride.
The shabads "mohan moh liya man mera
"3 is part of this romanticism. This romanticism is also very noticeable in other parts, of Sri Guru Granth Sahib Ji. E.g. when you read 'soul-bride' in Sri Guru Granth Sahib Ji, this is what it's talking about, this is what's happening behind the scenes. The actual word 'sohagan' just means 'bride' but given the divine nature of Krishna and the divine nature of this relationship with the Bhagat, it is translated as 'soul-bride'. Reference:: Sikh Philosophy Network http://www.sikhphilosophy.net/showthread.php?t=38559
But Mohan in the shabad you have posted is
referring to the eldest sahibzada of Guru Amardas ji, who took care of the pothi. If I remember correctly, he was in a state of samadhi and wouldn't pay any attention to Bhai Gurdas ji, who was sent first, and no attention to Baba Buddha ji who was sent after. Finally Guru Arjan Dev ji went himself and sang this serenade, thus attracting his attention to him, proving to the caretaker his humility and gaining respect as the Guru. Bhai Mohan came out and gave Guru Sahib the pothiyan after which Guru ji sang the 4th pauri blessing Bhai Mohan taht him and his whole family has been saved.
There's a bit more to it. Bhai Mohan being enlightened himself is (has become, merged with) Mohan as well. And you'll see both God/man, both Bhai Mohan and Mohan (karta purakh) being referred to as Mohan in the shabad. No need to separate them. Just as Satguru refers refers to God/Guru alike, so is Mohan in this shabad.
The fact that this serenade is to Bhai Mohan, becomes clear in the shabad quite early. Here:
ਮੋਹਨ ਤੂੰ ਮਾਨਹਿ ਏਕੁ ਜੀ ਅਵਰ ਸਭ ਰਾਲੀ ॥
Mohan ṯūŉ mānėh ek jī avar sabẖ rālī.
O Mohan, you believe in the One. Everything else is dust to you.
ਮਾਨਹਿ ਤ ਏਕੁ ਅਲੇਖੁ ਠਾਕੁਰੁ ਜਿਨਹਿ ਸਭ ਕਲ ਧਾਰੀਆ ॥
Mānėh ṯa ek alekẖ ṯẖākur jinėh sabẖ kal ḏẖārī▫ā.
You adore the One Lord, the Unknowable Lord and Master; His Power gives Support to all.
ਤੁਧੁ ਬਚਨਿ ਗੁਰ ਕੈ ਵਸਿ ਕੀਆ ਆਦਿ ਪੁਰਖੁ ਬਨਵਾਰੀਆ ॥
तुधु बचनि गुर कै वसि कीआ आदि पुरखु बनवारीआ ॥
Ŧuḏẖ bacẖan gur kai vas kī▫ā āḏ purakẖ banvārī▫ā.
Through the Guru's (Guru Amrdas's) Word, you have captured the heart of the Primal Being, the Lord of the World.
ਮੋਹਨ ਤੂੰ ਸੁਫਲੁ ਫਲਿਆ ਸਣੁ ਪਰਵਾਰੇ ॥
मोहन तूं सुफलु फलिआ सणु परवारे ॥
Mohan ṯūŉ sufal fali▫ā saṇ parvāre.
O Mohan, you have blossomed forth with the flower of your family.
ਮੋਹਨ ਪੁਤ੍ਰ ਮੀਤ ਭਾਈ ਕੁਟੰਬ ਸਭਿ ਤਾਰੇ ॥
मोहन पुत्र मीत भाई कुट्मब सभि तारे ॥
Mohan puṯar mīṯ bẖā▫ī kutamb sabẖ ṯāre.
O Mohan, your children, friends, siblings and relatives have all been saved.
ਤਾਰਿਆ ਜਹਾਨੁ ਲਹਿਆ ਅਭਿਮਾਨੁ ਜਿਨੀ ਦਰਸਨੁ ਪਾਇਆ ॥
तारिआ जहानु लहिआ अभिमानु जिनी दरसनु पाइआ ॥
Ŧāri▫ā jahān lahi▫ā abẖimān jinī ḏarsan pā▫i▫ā.
You save those who give up their egotistical pride, upon gaining the Blessed Vision of Your Darshan.
ਜਿਨੀ ਤੁਧਨੋ ਧੰਨੁ ਕਹਿਆ ਤਿਨ ਜਮੁ ਨੇੜਿ ਨ ਆਇਆ ॥
जिनी तुधनो धंनु कहिआ तिन जमु नेड़ि न आइआ ॥
Jinī ṯuḏẖno ḏẖan kahi▫ā ṯin jam neṛ na ā▫i▫ā.
The Messenger of Death does not even approach those who call you 'blessed'.
ਬੇਅੰਤ ਗੁਣ ਤੇਰੇ ਕਥੇ ਨ ਜਾਹੀ ਸਤਿਗੁਰ ਪੁਰਖ ਮੁਰਾਰੇ ॥
बेअंत गुण तेरे कथे न जाही सतिगुर पुरख मुरारे ॥
Be▫anṯ guṇ ṯere kathe na jāhī saṯgur purakẖ murāre.
Your Virtues are unlimited - they cannot be described, O True Guru, Primal Being, Destroyer of demons.
ਬਿਨਵੰਤਿ ਨਾਨਕ ਟੇਕ ਰਾਖੀ ਜਿਤੁ ਲਗਿ ਤਰਿਆ ਸੰਸਾਰੇ ॥੪॥੨॥
बिनवंति नानक टेक राखी जितु लगि तरिआ संसारे ॥४॥२॥
Binvanṯ Nānak tek rākẖī jiṯ lag ṯari▫ā sansāre. ||4||2||
Prays Nanak, Yours is that Anchor, holding onto which the whole world is saved. ||4||2||
In case the links don't work
1- page 335
2- page 998
3- page 1197