Etxea is the Basque word for home — the house, the hearth, the place you come from.
It is also hiding in plain sight inside the family name. The original Basque surname was Garaikoetxea, which Americanized over the years into Garacochea. The word for home was in the name the whole time.
Why it fits a bakery
Bread is the most domestic thing there is. It is made of three ingredients — flour, water and salt — it is eaten at a table, and for most of human history it was baked at home or a few doors from it. A little yeast helps the French breads along, and gives the sourdough a nudge in cold weather, but the sourdough does not need it.
A bakery that calls itself home is making a fairly specific promise: that the bread on the stall is the bread we would put on our own table. That is the only standard we have ever really used.