It's a Dracaena sanderiana (a.k.a., Lucky Bamboo). It is in no way any kind of bamboo (that's why we use Latin nomenclature). Many are grown completely in water, even though it is not an aquatic plant per se. Yes, it needs a bigger container, but I'd say it looks really healthy. You are essentially growing it hydroponically, which is fine. If you want to feed it, use no more than half strength of a liquid fertilizer (many of us are going into winter in this hemisphere).

a plant will surely show you when it needs help ... and your looks great ... dont screw it up trying to fix what probably isnt broken ...

i might go 1/4 or even less strength on the water sol fert ... you can always add more.. but you cant remove excess ...

when using it.. focus on the pot size.. not the plant size .... we dont want fert salt buildup in that tiny pot ..

watch a couple of these vids.. and make a few new pieces.. just in case stuff happens

https://duckduckgo.com/?q=Dracaena+sanderiana+propagation&t=ffcm&iax=videos&ia=videos

ken

Agree with lucky bamboo, D. sanderiana/braunii. If it ain't broke, don't fix it. It looks very nice, happy. I would keep doing what you have been doing.