I believe what I have is Eu.rhipsalis.
It's very leggy and flops. I read the it is a tree type so I am wondering what to do to train it into a tree rather than a trailing sad sack.
I think it has to be either a Euphorbia or a Rhipsalis. Not both. It looks like a Rhipsalis - I don't think you can make it stand up. Its doing what they do.
Is the name supposed to be Euphorbia rhipsaloides? If so, that is now a variety of tirucalli. I have no idea if that variety is supposed to be upright, but the regular tirucalli is a big tree. Your plant looks quite unlike the tirucallis that I know. Whatever you do, be very careful of the sap (eg. when cutting branches) as it is likely to be a severe irritant, bad even for a Euphorbia. Leggy, floppy plants generally benefit from some strategic pruning and greater exposure to sunlight. I don't know how you are growing your plant now so these are just some ideas.
Could it be Rhipsalis salicornioides
I thought the name was changed from Rhipsalis to Hatiora salicornioides a number of years ago.
Wikipedia says its 'also called Hatiora Salicornioides' but I think it is the most commonly used name judging from what a Google search brought up. It's an interesting plant. May need to find one.
There has been one in my family for over thirty years. It was my mother's and became mine when she passed. It originally lived on a table, under the deep overhang of our pool patio, when I was growing up. Many offspring later, I have more than enough to share. DM me. It blooms in a sunny spot come mid-winter. I have shared pieces with several other DGers over the years.
Before Laurel made her generous offer I had one on the way from Ebay. It arrived and its a cute little plant. I need another like a hole in my head but I do like hanging cactus so this should be easy to find a place for.