Staghorn fern. Cool plant. Here is a link that might be useful: photo of a staghorn fern

I think your K. delgoensis is Bryophyllum daigremontianum, commonly called "alligator plant".

You didn't say what yo are planning on using to repot. If you are getting bagged soil, get a bag of perlite. If you can get pumice easily, that would be great instead. Sift it using a kitchen sieve to get rid of the dust & smallest particles, and mix 50/50 with soil. Plant needs good drainage (all succulents do), and good light as mentioned.

Definitely could use more light. Looks to be an elongated Corpuscularia lehmannii. Is yours in the same mix that it came with? Is it just the lanky growth or is there something else going on with your plant?