What is the one-point compactification of the Loch Ness Monster? The Loch Ness Monster surface is the noncompact orientable surface with one end accumulated by genus. If we take the one-point compactification of this surface ~~we get some surface with finite genus by the classification.~~ and get a manifold, it would have finite genus by the classification. This seems a little absurd. What is the one-point compactification of the Loch Ness Monster, and in general, is there any intuition behind determining compactifications of surfaces with infinite genus?

This space (the one-point compactification) is not homeomorphic to any of the "standard" spaces you encounter in your topology classes (in particular, it is not a surface). Just call it "the one-point compactification of the Loch Ness Monster" (OPCOLNM), if you are looking for a nice name. As for the intuition of such spaces, I do not know what to say, there is none as far as I know. You may want to read some papers on the classification of noncompact surfaces, which uses compactifications to classify these. See my answer here for a reference and some discussion where I describe the "end compactification" in concrete terms.