For example, with the piano, you might be able to say that you can consistently play a certain song from memory with occasional mistakes, while having trouble learning new pieces quickly (if you might have difficulty sight-reading).
For a language, you might be able to say that you can have a half-hour conversation without using English/your native language without too much difficulty, but you can't speak about technical or philosophical topics, and you might still be working on understanding how to use certain grammatical tenses.
Then, there's less reason for doubt from other people or yourself, as your skill level is communicated more objectively and less subjectively. The framing also gives you a nice clear path for what to work on next (for example, learning how to talk about a specific topic and understand a new grammar tense).
If one is fine with that, then yes, call oneself a pianist I guess?
Personally I'd say I was "learning to play the piano".
Or what about someone says: "I'm a Software Engineer" ... but then can't write the first characters in a FizzBuzz solution and wonders "what's a for loop?"