For a better chance of getting an exact id, I'd suggest posting on this forum; bambooweb.info • Bamboo Forum

All I can say is that it does appear to be a Phyllostachys of some type, because it does appear to have the groove ("sulcus") which appears on alternating sides of the culm, switching side at each node. The green culm with a hint of yellow in the sulcus makes me think P. aurea "flavescens inversa" or Phyllostachys vivax 'Huanvenzhu'. With P. aurea, you usually get some close together nodes near the bottom of the cane.

Although yours is certainly not the yellow crookstem bamboo (P. aureosulcata) taht is famously invasive in New York, pretty much all species of Phyllostachys are likely to be pretty invasive in your climate. Yes, mowing (or browsing by animals) will in principle stop it spreading, but you need to able to mow a good 12 foot band all the way around it, and even then be alert for it coming up twice that far away. Garden walls won't stop it, they can spread up to about 2 feet below the surface, and push their way between gaps between stones. People who are serious about stopping bamboo put in reinforced concrete undergound barriers to a depth of about 3 feet deep.

Unfortunately growing running bamboos in climates where they really do run is potentially a liability, unless you can really isolate them to keep them in a clump. P. aurea has taken over entire hillsides in the Azores.