If you are an Idealistic Solipsist, is it not true that you must say "I am a Solipsist." or "I am the Solipsist."?
One cannot say "I am one of the Solipsists" for example. Are there other counterexamples?
Solipsism can be more subtle than that, Berkeley's for example, although there is a linguistic disagreement on whether to classify his philosophy as solipsism, and Berkeley denied the label. Basically he contends that "to be is to be perceived" (esse est percipi), there is no material or physical substrate to that, and each soul has a whole perceived world all to itself. In this Berkeley anticipated Kant's idea of appearances (phenomena).
This does not mean that there can be no other souls however. According to Berkeley God is one of them, and so are other people. God produces perceptions in each other soul independently however, so there is no shared world in any sense, and they are all solipsists. See Grey's The Solipsism of Bishop Berkeley.
Wittgenstein makes a cryptic remark in the Tractatus, which is perhaps the only "endorsement" of solipsism by a major philosopher
"In fact what solipsism intends is quite correct, only it cannot be said, but it shows itself. That the world is my world shows itself in the fact that the limits of language (the language, which I alone understand) means the limits of my world."
According to Hintikka's On Wittgenstein's `Solipsism', the parenthetical phrase is a mistranslation, and should instead read "the only language that I understand". He also argues that what Wittgenstein thought solipsism intends to say is different from what most philosophers take it to say.
If you are a solipsist, from your point of view you would only be talking to yourself anyway. So you could say whatever you wanted.
If you are a (presumably external) interlocutor trying to catch a solipsist in an implicit contradiction, there will probably be plenty of opportunities. Even if the solipsist has no actual belief in the existence of others, the solipsist still needs to behave and speak as if the solipsist does believe in their existence to make any progress at all through this illusion we call life.
If solipsism is the thesis that only I exist, then Berkeley was certainly not a solipsist since a major burden of his argument in the Principles is that all that exist are his and other minds or spirits and their ideas. Spirits crucially include God; and while Berkeley was a Bishop I don't believe he credited himself with divinity.
I don't think 'Idealism' comes into the picture. It is indifferent to solipsism whether the 'I' that alone exists is mental, spiritual or material. But your question suggests possibilities for plurality, paradoxical as that might appear.
How so ? Like this. It is a logical possibility that while only I exist, I consist of multiple selves, minds or spirits. (This is nothing like Berkeley's account.) Being the only thing that exists does not exclude having a plural identity. See Kathleeen V. Wilkes, Real People: Personal Identity without Thought Experiments, ISBN 10: 0198249551 / ISBN 13: 9780198249559, Oxford University Press, 1988 : 109-128.