I think its a not very well Plumeria, judging by the shape of the veins in the leaves which are clearly revealed because of the yellowing inbetween them, but its hard to tell for sure because it's not growing as it should, whatever it is. Note that the yellow discoloration between these veins indicates a severe magnesium shortage, leaves should all be green. Plumeria is frangipani and has beautiful flowers - when grown correctly. Houseplant, minimum 50deg F in winter, bright light with some direct sun, water liberally spring to autumn, sparingly in winter. Repot in spring every 2 years - I suggest you repot immediately, in new compost and possibly a larger pot - these plants get large, reaching 6 feet, and do best in a conservatory. Otherwise, it needs a good dose of Epsom salts, preferably in the next ten minutes...

Sorry, Bamboo, but it is actually a Croton, aka Joseph's Coat (Codiaeum variegatum).
Walkytalky, this one could be transplanted, and will probably grow branches if you do, but it won't really need it for another year or so. I would let the top cm or so of soil dry between waterings, and make sure that it has good drainage. Any good houseplant food is fine by it, so just use your favorite. It grows best in bright light, within 1 meter of a window, maybe with some morning or filtered sun, but it doesn't get all the shades of gold, orange, and red, until it is in relatively low light conditions. Commercial growers grow them in one greenhouse, then move them into a darker one for a couple months to color up, before sending them to the retail shops. It can be put outside in the shade, as long as the nights arent below 13º F.

I did look at Codiaeum, but my pic of it doesn't show the veination very clearly, and doesn't really look like this one, so I plumped for Plumosa. Does that mean the veins should be showing as clearly as they do tugbrethil?

It depends on the variety, Bamboo. This one looks like 'Mosaic', minus the conditions needed for full color. Other varieties, such as the ubiquitous 'Petra', look quite different!