Your plant looks like a ponytail palm that has had its top cut off and has responded by sprouting multiple branchlets. I don't know what its currently most correct botanical name is but it is widely known as Beaucarnea recurvata. They make great house plants but you have to be careful not to keep them too wet. Yours with so many shoots should turn into a really interesting looking plant. mplant
You are absolutely correct - it is Ponytail Palm, I have been able to find some information about caring, hopefully, there will be enough sun indoors for it. Thanks very much for your help.
