Brace yourself, for a "Leo Book Length Essay", I apologize, read it in chunks. Short answer: Phyllostachys aurea - Golden Bamboo. Scroll on for the gory details.
Nice, first a little terminology, what used to be called a cane, the more accurate term is culm. Culms normally are hollow, and at the nodes, an internal partition seals this hollow (septum). Nodes are the points where branches come off the culm. They are ridged, or have a ridge, marking the location of the partition or septum. Different species will have a single ridge, or double ridges marking the node. Internode is the distance between the nodes, where branches come off the culm. There are various hairs on leaves and stems, which are used to narrow down to species. The American Bamboo Society has an excellent website, browse thru it, and you can possibly get to exact species. I'll try to get you to genus and species. You do have a true bamboo, not some grass. Check internet images of the species I suggest, and see if you agree.
Feel the culm, is there a single groove that runs the length of the internode, usually alternating between sides of culm after each node? If yes then the genus is Phyllostachys. No, it could be a number of genera. The congested pattern of the nodes at the base of your largest culms suggest a few candidate species. So we'll go from these markers. ( for those playing a long at home, this is my thought process )
Culms grooves present =
Phyllostachys genus, - Phyllostachys usually has 2 unequal size branches at a node in addition, the culm groove is present. The long running rhizome also suggests genus Phyllostachys. All Phyllostachys have a running habit. New culms can be as much as a meter away from the previous if planted in the ground. Never plant it ''loose'' in the ground, if it is happy in your climate it will become wildly invasive. Always install a rhizome barrier before planting in the ground. Many of the Phyllostachys are fairly winter hardy. Some will tolerate extreme cold. I have 3 species of Phyllostachys growing in outdoor beds, that receive no winter protection, and they survive my Chicago winters just fine. (low temperatures of -35 C or -20 F are not unusual here). They are fast growing, a planting of Phyllostachys will show mature behavior in as little as 5 years, they have good visual impact and are my favorite group of bamboos for being easy to grow. Not the easiest to keep happy in flower pots, but if given a 3 meter by 3 meter space in the ground (with proper barriers) they will grow to full height for the species in as little as 5 years. In 3 years you can get half or more of mature size. And virtually all Phyllostachys are good to eat. Bamboo shoots, delicious, especially dug fresh, blanched then either steamed or stir fried.
The more I look at your photo, the more I am confident it is a Phyllostachys, and I'm pretty certain it is one specific species.
The congested irregularly spaced nodes at the base of the largest culms suggest that the most likely candidate is
Phyllostachys aurea, Golden Bamboo, which is actually plain green. Culms as they age turn a lighter yellowish green in full sun, in full sun locations, the culms eventually mature to a clear yellow their third or fourth year. In shade they will remain green. This is a cold hardy running bamboo. Foliage should stay evergreen in winter, well below freezing. Foliage damage should not be serious to about -10 C or +5 F, In weather colder than these temperatures, the bamboo will ''Top Kill'', but the rhizomes 15 cm or 6 inches or more, under the soil should be able to sprout in spring to temperatures of -16 C or +0 F. Maximum height in a mild climate would be about 8 or 9 meters, roughly 27 feet. In climates where growing seasons are shorter than 150 days, maximum height will be lower. If this bamboo has been indoors or in a greenhouse, do not expose it suddenly to extreme cold, it needs a month or two to adapt. They are native to a large area of China, parts are fairly subtropical, you should be able to winter indoors for the remaining winter, put it outdoors in spring. If your winters are warmer than -10 C, or above +5F, you could grow it in an outdoor bed, top dress the bed with 15 cm of leaf mulch before winter and let it get buried by snow, it should be fine. In an above ground container it will not be as hardy. If you grow it in a container, leave it outdoors until it has had a few frosts, then winter it in a cool sunny window, or winter in a cold spot where you would winter deciduous or pine bonsai. If temperatures are below +4C, and above 0C that would be perfect for cold storage. Below 4 C they do not need light, even though they have leaves. But they don't need as much cold in winter as a maple tree would need. You can run it indoors, in a bright window, in a cool house. Less than 18C would be fine, closer you get to +4C the more vigorous your spring flush of new shoots will be. Wintered warm the flush of growth is more staggered, less synchronous, but it still grows reasonably well.
No culm groove = these are 2 candidates.
Pseudosasa
japonica 'Tsutsumiana' - usually only one branch at a node, no culm groove, culm feels round. Running habit, swollen at base of internode, like a "Buddha Belly", a variant of Japanese Arrow Bamboo. Your photo shows irregular internode lengths, normally Pseudosasa japonica has a very uniform internode length. Probably not what you have, but included the name for you to check images, just in case. This is a temperate to sub-tropical bamboo, winter hardiness is similar to Phyllostachys area, maybe a little less hardy, but over all pretty similar. Tends to be shorter, less than 7 meters, often less than 4 meters.
Bambusa
vulgaris 'Wamin' - Bambusa has no culm groove, internode feels round. At the nodes will have many branches, especially on culms over a year old. One or three of the branches will be significantly larger than the rest. This bamboo tends to have a clumping habit, new rhizome will not run for any distance. (a few inches or centimeters, not feet or meters). The species form is a true tropical timber bamboo, capable of reaching 15 meters or so, but the cultivar 'Wamin' is a dwarf form, normally topping out at 3 meters. I do not think this is the bamboo you have, I did not see enough branches at the nodes, and the running rhizome really looks like a Phyllostachys rhizome.