It is a clumping timber bamboo that does not spread. Species name is: Old Hammii

I was told in my neighborhood in Cali that we can't have nothing but trees that go over the fence line height, , can this be considered a tree

This is Bambusa oldhamii it is a clumping bamboo but it can spread or "clump" 6 in. a year I would specify a HDPV Root Barrier to keep it at bay. This is technically a grass and it can be sheared or kept at a certain height. I would use a bamboo that only grows as high as you want.

vmarkey: With our planter boxes, which can be custom sized, you can plant any type of bamboo to be planted to provide your property's privacy border. They can be ordered to roll or to be stationary. We purveyed multiple installations for such use. It does not matter if you order clumping of spreading species. Other trees and shrubs can also be planted in our boxes. See images below of boxes. References upon request. Site: http://www.rollingplanter.com

You might enjoy this houzz read. https://www.houzz.com/magazine/small-garden-you-can-still-do-bamboo-stsetivw-vs~13023263