Is there a benefit to having more than one of the same monster?

[Mallomar]

I currently have two regular noggins, and have a fwog egg when I already have a fwog. Should I be looking to keep them for some reason, or is it better to sell them and get a variety?

[AteBallEight]

Go for monster variety first to complete an island's song while taking up the least amount of available Beds. Once you reach a certain level you can also buy a Hotel and check in monsters to save Beds.

Otherwise, the biggest benefit of placing more than one of a monster is to gain more Coins when you check in the game. However, it's better to do that with higher element and rarer monsters as they make the most money. You'll also find that more monsters of a single type = increased volume of their track in the song.

[krunjar]

Mostly aesthetics but it's not wise to keep loads of low level monsters since they don't make you much due to low coin max. The natural islands have room for heaps of monsters if you can afford the diamonds to fully upgrade them. They cap out at 180 beds. Most of the other islands cap out at 90.

[123]

As others said, 1 each is best, sell all your doubles. Except quad-elements, these are your coin-producers. So if you go for the full song, go for 1 monster each, but fill the rest of the available space with quads, because these give you most coins/got the highest coin-capacity.
There are some exceptions like "legendary" monsters you buy for relics, which have an even better rate than quads, also epics and rare quads are better than normal quads. But this is not that important in the beginning, coin-farming with quads is a simple and working strategy so I'd breed many of these and 1 of everything else.