I recently heard a terrible argument arguing that Simon means "grain of sand" and that when Jesus changed Simon's name to Peter, he was changing this grain of sand into a Rock. Obviously, as you might guess, this argument came from someone who thinks that Peter was the first pope.
There are two significant problems with this argument.
First, "Peter" didn't replace "Simon" it became a sort of surname, essentially replacing "Barjonna" although he continued to be called "Barjonna" even after being called "Peter." We can see this from the following:
Mark 3:16 And Simon he surnamed Peter;
John 1:42 And he brought him to Jesus. And when Jesus beheld him, he said, Thou art Simon the son of Jona: thou shalt be called Cephas, which is by interpretation, A stone.
Matthew 4:18 And Jesus, walking by the sea of Galilee, saw two brethren, Simon called Peter, and Andrew his brother, casting a net into the sea: for they were fishers.
John 1:40 One of the two which heard John speak, and followed him, was Andrew, Simon Peter's brother.
Luke 5:8 When Simon Peter saw it, he fell down at Jesus' knees, saying, Depart from me; for I am a sinful man, O Lord.
John 6:8 One of his disciples, Andrew, Simon Peter's brother, saith unto him,
Matthew 10:2 Now the names of the twelve apostles are these; The first, Simon, who is called Peter, and Andrew his brother; James the son of Zebedee, and John his brother;
Luke 6:14 Simon, (whom he also named Peter,) and Andrew his brother, James and John, Philip and Bartholomew,
John 6:68 Then Simon Peter answered him, Lord, to whom shall we go? thou hast the words of eternal life.
Matthew 16:16 And Simon Peter answered and said, Thou art the Christ, the Son of the living God.
John 13:6 Then cometh he to Simon Peter: and Peter saith unto him, Lord, dost thou wash my feet?
John 13:9 Simon Peter saith unto him, Lord, not my feet only, but also my hands and my head.
John 13:24 Simon Peter therefore beckoned to him, that he should ask who it should be of whom he spake.
John 13:36 Simon Peter said unto him, Lord, whither goest thou? Jesus answered him, Whither I go, thou canst not follow me now; but thou shalt follow me afterwards.
Mark 14:37 And he cometh, and findeth them sleeping, and saith unto Peter, Simon, sleepest thou? couldest not thou watch one hour?
John 18:10 Then Simon Peter having a sword drew it, and smote the high priest's servant, and cut off his right ear. The servant's name was Malchus.
John 18:15 And Simon Peter followed Jesus, and so did another disciple: that disciple was known unto the high priest, and went in with Jesus into the palace of the high priest.
John 18:25 And Simon Peter stood and warmed himself. They said therefore unto him, Art not thou also one of his disciples? He denied it, and said, I am not.
John 20:2 Then she runneth, and cometh to Simon Peter, and to the other disciple, whom Jesus loved, and saith unto them, They have taken away the Lord out of the sepulchre, and we know not where they have laid him.
In these verses we see that Simon is referred to frequently as "Simon Peter" or by similar labels, such as "Simon, whom he also named Peter" (where "also" implies that this was an additional name) and "Simon he surnamed Peter" (where "surnamed" implies that an additional name was imposed upon Simon). Finally, while we see a large number of verses (not reproduced above) where Simon is simply referred to as "Peter," we never see Simon referred to as "Peter bar-Jona" or "Peter the son of Jona" or the like. Thus, Simon's name wasn't changed: he was given an additional name that essentially took the place of his natural name.
A second significant problem is that "Simon" doesn't mean "grain of sand" - it means "heard." The Greek word that we translate "Simon" is Σίμωνα (Simona). This Greek word is a borrow word from Hebrew. The Hebrew word to which it (as well as the alternative Grecianized form Συμεὼν (Simeon)) corresponds is שׁמעון (Shimon) which is etymologically derived from the word שׁמע (Shama) which is the root word for "to hear." With some words, the etymology is a bit speculative, but not with this one:
Genesis 29:33 And she conceived again, and bare a son; and said, Because the LORD hath heard that I was hated, he hath therefore given me this son also: and she called his name Simeon.