What will happen is that you will make Escoffier cry. Nothing more.
In a more serious tone, the naming of sauces is somewhat arbitrary/tradition driven. There are five mother sauces, Hollandaise being the only emulsion among them. All other sauces are derived for them, making Mayonnaise a Hollandaise derivative. There are hundreds of derived sauces, and the difference is always slight. The use of butter instead of oil (or the other way round) would be enough for the result to be considered a completely new sauce, neither mayonnaise nor hollandaise. While it is a common occurence in home kitchens, I don't think there is an official name for these switched versions. Some cooks even use the name Mayonnaise for a pure water-yolk-veg oil emulsion, without the mustard and vinegar (for example Ruhlman in Ratio).
Technically, there is no reason not to do it. The slight difference of water to fat ratio when you are using butter shouldn't matter. A yolk can emulsify lots of fat, and the amount of fat you use per one part water is mostly a matter of taste. So you can go ahead and substitute butter in a mayonnaise recipe. The taste will be different, but you will be as successful as with a normal mayonnaise. Only remember to serve it warm, I would expect it to harden a bit when cooled.