No, you should not name your guardian Angel, his name will be revealed to you in Heaven, if you make it.

Your guardian angel does not want to be called Doug or Frank, God gave him a name, and God will reveal it to you if you make it to heaven, but it is not His will for us to know it on earth.

As for angels sharing names in Heaven, I highly doubt it, each angel is it's own species according to St. Thomas. I suppose it's possible, but I highly doubt it.

Fr. Ripperger has a really good talk on this, the best I've ever heard on the angels:

It might be, but in the case of the damned it would only be revealed to them to further increase their punishment in Hell since those in Hell detest all that is holy and good, so it would be an even greater suffering for them to know the name of their guardian angel. So it is possible, but we can't know for certain.

That's correct. Once the soul has been judged, the angel's assignment is complete and it will just enjoy the delights and pleasures of Our loving God for eternity. Fr. Ripperger discusses that at the end of the talk I believe. If you are in Heaven, you will enjoy your guardian angels company for eternity, if you enter Hell, the guardian angel will have completed the task assigned to him by God and enjoy the rewards of heaven regardless.

There are probably trillions of angels is my guess because each person has their own particular guardian angel assigned to them. I am almost certain that guardian angels do not "go onto the next person." Guardian angels are low ranked angels, so their mission from God is very particular, while higher ranked angels do more broad tasks that could last for many thousands of years, like St. Michael for instance.

A little more info on angels monka966.

‘The angels were created in the empyrean heavens and in the state of grace by which they might be first to merit the reward of glory. For although they were in the midst of glory, the Divinity itself was not to be made manifest to them face to face and unveiled, until they should have merited such a favour by obeying the divine will. The holy angels, as well as the bad ones, remained only a very short time in the state of probation; for their creation and probation with its result were three distinct instants or moments, separated by short intermissions. In the first instant they were all created and endowed with graces and gifts, coming into existence as most beautiful and perfect creatures. Then followed a short pause, during which the will of the Creator was propounded and intimated, and the law and command was given to them, to acknowledge Him as their Maker and supreme Lord, and to fulfil the end for which they have been created. During this pause, instant or interval, Saint Michael and his angels fought that great battle with the dragon and his followers, which is described by the apostle Saint John in the twelfth chapter of the Apocalypse. The good angels, persevering in grace, merited eternal happiness. The disobedient angels, rebelling against God, merited the punishment, which they now suffer…. Mary of Agreda'a ‘The Mystical City of God’ or ‘The Divine History and Life of the Virgin Mother of God.’

‘In attendance upon the Divine Majesty, thus enthroned, are vast hosts of angels, who are divided into three hierarchies, one serving in the empyrean, one in the heavens between the empyrean and the earth, and one on the earth. Each of these hierarchies is divided into three choirs, or orders; the first, into the orders of Seraphim, Cherubim, and Thrones; and the main occupation of these is to chant incessantly – to “continually cry” the divine praises. The order of Thrones conveys God’s will to the second hierarchy, which serves in the movable heavens. This second hierarchy is also made up of three orders. The first of these, the order of Dominions, receives the divine commands; the second, the order of Powers, moves the heavens, sun, moon, planets, and stars, opens and shuts the “windows of heaven,” and brings to pass all other celestial phenomena; the third, the order of Empire [rather Powers or Authorities], guards the others [warrior angels].
     ‘The third and lowest hierarchy is also made up of three orders. First of these are the Principalities, the guardian spirits of nations and kingdoms. Next come Archangels; these protect religion, and bear the prayers of the saints to the foot of God’s throne. Finally come Angels; these care for earthly affairs in general, one being appointed to each mortal, and others taking charge of the qualities of plants, metals, stones and the like. Throughout the whole system, from the great Triune God to the lowest group of angels, we see at work the mystic power attached to the triangle and sacred number three – the same which gave the triune deities in Egypt, and which transmitted this theological gift to the Christian world, especially through the Egyptian Athanasius.
     ‘Below the earth is hell. This is tenanted by the angels who rebelled under the lead of Lucifer, prince of the seraphim –the former favourite of the Trinity; but, of these rebellious angels, some still rove among the planetary spheres, and give trouble to the good angels; others pervade the atmosphere about the earth, carrying lightning, storm, drought, and hail; others infest earthly society, tempting men to sin; but Peter Lombard and St Thomas Aquinas take pains to show that the work of these devils is, after all, but to discipline man or to mete out deserved punishment.' ---  Andrew D. White: A History of the Warfare of Science with Theology in Christendom, New York, Appleton, 1870          

When soul is sent to purgatory, where does its guardian angel go and what does it do?

Do theologians agree regarding the test given to Lucifer by God in the empyrean heaven?

A priest told me all the angels were given the same test, which consisted of being shown the infant Jesus and given the command to kneel down and pay Him homage - without being told Who He was or why He appeared that way.  Roughly one third of them including Lucifer were not willing to do so;  knowing the consequence of their disobedience they made the act of will to refuse anyway;  their choice was permanent and irredeemable, which is why they cannot escape hell forever.

When Lucifer and his cohort were struck down to hell, was hell already created or God created it at that instant?

I have also heard that according to St. Louis de Montfort, Satan fell from Heaven because he would not serve our Blessed Lady, especially because of the fact that God revealed to him that there was going to be a woman who would so outstrip him in grace. I wonder if that is why the snake in the Garden of Eden went after Eve first, thinking that she might be the Blessed Virgin Mary or he was just simply filled with hate toward women after God’s revelation.