Is there a co-relation between the name or Bethlehem and Jesus' teachings? Bethlehem, the birth-place of Jesus literally means 'house of bread' . It is possible that the town had a good concentration of bakeries, from which oven-baked bread of prized quality was bought by the people of adjoining areas. It looks coincidental that Jesus frequently used the image of 'bread' in His teachings, culminating in the institution of Holy Eucharist. I wish to know if any studies have been made by the Catholic Church on the co-relation of the name of Jesus' birth place and His teachings in which bread plays a prominent part.
Has there been a formal study done by the Church? Not necessarily. But there are plenty of books and articles and homilies and podcasts on the topic:


Blogs: 


desiringgod.com - Bethlehem: House of Bread
archspm.org - I know Jesus was born in a manger, but why is that important and what does it mean? 

Books:


The Eucharist: A Bible Study Guide for Catholics
Jesus and the Jewish Roots of the Eucharist: Unlocking the Secrets of the Last Supper
The Hidden Manna: A Theology of the Eucharist
The Lamb's Supper: The Mass as Heaven on Earth
Consuming the Word: The New Testament and The Eucharist in the Early Church 

Podcast:


https://catholicstuffpodcast.com/podcast/2011/06/30/how-transubstantiation-works.html



The short answer is yes, the name 'house of bread' has significance when relating to His other teachings. Christ was born in a manger in the town 'house of bread.' Let's break that down.

What exactly is a manger? A manger was used as a feeding trough for the swine. So the obvious significance here is that Christ was born and immediately laid in a place where food is eaten from. Think of the symbolism here: Jesus would institute the Eucharist, His own flesh and blood for us to consume, the same flesh and blood that was born into a feeding trough. And where was that feeding trough? The house of bread! His flesh would be presented in a trough for us to eat under the disguise of bread. Manger in the house of bread, Bread of the Eucharist on the altar. 

Another point, 'manger' comes from a French word that means 'to eat.' When translated from Greek, John chapter 6 uses the same word when Jesus says to eat (or chew) his flesh. (https://fellowshipoftheminds.com/2012/12/30/the-meaning-of-jesus-being-born-in-a-manger/)

There is also some symbolism about Him being born into a feeding place of swine because the Jews could not eat pork, but that is for another topic...