Can a discoverer give the name he wants to his finding?

Let's assume that some scientist discovers a phenomenon that has never been noticed before.

He wants to write a paper about it but he doesn't want to constantly write "effect of change of some properties blahblahblah". Can he therefore name this effect with a name of his choice? For example "Discoverer's name's effect". Or "fluffy puppy effect" (just because he likes puppies)?

The same for constants. Can one name newly discovered constant "my name constant"?

This question can be simplified to: "what are standards for naming new physical entities?"