You are PETER, and on this ROCK I will build my church

[TonyChanYT]

In the OT, the rock is often used to refer to God, Psalm 18:

2 The LORD is my rock, my fortress and my deliverer; my God is my rock, in whom I take refuge, my shield and the horn of my salvation, my stronghold.

This metaphor is repeated in the NT, 1 Corinthians 10:

4 and drank the same spiritual drink; for they drank from the spiritual rock that accompanied them, and that rock was Christ.

Jesus was gracious when he spoke in Matthew 16:

18 I tell you that you are Peter, and on this rock I will build my church, and the gates of Hades will not overcome it.

Peter,
Πέτρος (Petros)
Noun - Nominative Masculine Singular
Strong's 4074: Peter, a Greek name meaning rock. Apparently a primary word; a rock; as a name, Petrus, an apostle.

rock
πέτρᾳ (petra)
Noun - Dative Feminine Singular
Strong's 4073: A rock, ledge, cliff, cave, stony ground. Feminine of the same as Petros; a rock.

HELPS Word-studies

4073 pétra (a feminine noun) – "a mass of connected rock," which is distinct from 4074 (Pétros) which is "a detached stone or boulder" (A-S). 4073 (pétra) is a "solid or native rock, rising up through the earth" (Souter) – a huge mass of rock (a boulder), such as a projecting cliff.
4073 (petra) is "a projecting rock, cliff (feminine noun) . . . 4074 (petros, the masculine form) however is a stone . . . such as a man might throw" (S. Zodhiates, Dict).

What is the meaning behind Jesus giving Simon the name Peter?

Peter, the little rock, was compared to the big rock of the foundation. It's a pun in Greek.

What is the significance behind Jesus giving Simon the name Peter?

It showed how gracious Jesus was to Peter using a pun. Also, the Holy Spirit used Peter to start the nascent church. Peter gave a sermon on Pentecost, and 3000 souls were saved in Jerusalem (Acts 2:41). Peter and John went to Samaria and laid their hands on some believers for them to receive the Paraclete/Spirit (Acts 8:17). Peter preached in Cornelius' house. He was a gentile. The Holy Spirit fell on the gentiles (Acts 10:47).