Ibn Kathir reports that Abd al-Muttalib invited the people of Quraysh to enjoy the feast after making the sacrifice in celebration of his birth, and they asked his name.
“I have named him Muhammad” he replied.
“Why?...”, they asked.
“Because I wanted God to praise him in heaven and His creatures to praise him on earth.”

And indeed this sentiment is echoed in the Quran itself, wherein Allah subhanahu wa ta’ala says:

Lo! Allah and His angels shower blessings on the Prophet. O ye who believe! Ask blessings on him and salute him with a worthy salutation. [Ch. 33 Vr. 56]

A contemporary munshid wrote:

For his name is Ahmad and Muhammad
He is praised in heaven and praised on earth
Though no praise can reach to his true worth
Send peace on him and his family.

His names reflect his nature, for he is praised in every place and in every age, by the residents of the heavens and the earth alike. Every corner of this globe now holds people who accept his message and worship Allah subhanahu wa ta’ala alone, and thus recognize his status as the final Messenger of God. And so no moment passes as the day turns to night in one part of the world or the night turns to day in another part, but he is being praised, his name is being uttered and peace and blessings are being sent upon him.

This continuous, collective praise which rings out the world over - whether in silent prayer or reverberating chant, all heard clearly in the heavenly realm - is simply one manifestation of the limitless love that is felt towards the Beloved of Allah, Muhammad . And that love is an undeniable, necessary tenet of our religion.

In fact Allah subhanahu wa ta’ala Himself censures the one who loves anything more than Allah and His Messenger, saying in the Noble Quran:

“Say: If your fathers, your sons, your brothers, your wives, your tribe and your possessions you have earned, commerence you fear may slacken, dwellings you love – if these are dearer to you than Allah and His Messenger and to struggle in His way, they wait until Allah brings His command.” [Ch. 9, Vr. 24]

And the Prophet said, “None of you will believe until I am dearer to him than his own soul.”

It’s clear from this and similar reports that loving the Prophet is something necessary to true belief, and anyone who has experienced a deep love will attest that it is a limitless ocean of feeling the depths of with are often impossible to plumb. The emotion and act of loving is something to which volumes of poetry have been dedicated and lifetimes have been spent philosophizing in trying to determine its reality.

With such concepts that are so difficult to define, and perhaps best left undefined, such as love, the best way to recognize it can be through its signs. And the signs of love for the Prophet are clearly seen in his companions, whose descriptions of him read like poetry and whose actions are a testament to limitless love. They left their homes and families for the love of Allah and His Messenger, they fought and died for him, and when he left them and this world they were as forlorn lovers pining after the beloved.

When Bilal (ra) approached death and his wife cried out in sorrow, his response was “What joy! I will meet those I love, Muhammad and his party!”Out of sorrow he had stopped calling the adhan after the death of the Prophet, save at the special request of his blessed grandson (ra), since such reminders of times with the Prophet were too painful. Yet, the only joy to be felt again was at the thought of being reunited with him through death.

Abu Sufyan (ra) in times of enmity had remarked “I have not seen any people who love anyone the way the Companions of Muhammad love Muhammad.”
Qadi Iyad (rh) sets out eleven signs of loving the Prophet which are worth noting and measuring oneself against, they are:
1.Emulating him by following his sunnah.
2.Preferring his verdict to one’s own desires.
3.Only getting angry for the sake of Allah (as the Prophet did this)
4.Mentioning him often.
5.Yearning to meet him
6.Mentioning him with exaltation and respect, being humbled when he is mentioned.
7.Loving those who love him , and loving his Ahlul Bayt and his sahaba (ra).
8.Hating anyone who hates Allah and His Messenger
9.Loving the Quran which he brought.
10.Having compassion for his community; giving them good counsel and striving for their best interests.
11.Preferring poverty to the things of this world.

Perhaps the best expression of the unlimited nature of this love is in the words of Imam Busiri who said:

Leave what the Christians have said about their Prophet!
And then affirm what you will in praise, and do so with excellence.

As long as the wrongful claims of partnership with God or other forms of deification are cast firmly aside, since they are unthinkable and against the very foundation of religion, then after such negation of there being any God but Allah, there is unlimited room for praise and love for the Prophet

There is no such thing as “over-exaggeration”, since how can the praise be exaggerated for one whose rank is so great that it can never be known by other than his own Creator. No words of praise, no depth of love can be too much, since as Hassan ibn Thabit said, words to not praise him , rather his mention makes the words praiseworthy. And man’s love for his own soul and his own desires sees no end in sight, how many a man sells his Hereafter for his desires, and how many a man abandons this worldly life to safeguard his soul’s eternal life? How then, if true belief is loving the Prophet Muhammad more than one’s own soul, can anyone attempt to place limits on that love?

References

Al Quran Al Kareem
Al Sira al Nabawiyya, Ibn Kathir
Ash Shifa, Qadi Iyad
Imam Busiri, Qasida Burda
Talib al Habib, Hilya (Portrait of the Prophet)