In Japan “vegetarian” has no fixed meaning. A dish sold as ベジタリアン can still be made with fish stock, egg or dairy. ベジタリアン often means “no meat”, sometimes “no meat or fish”, rarely “nothing animal”. ヴィーガン (vegan) is better known in Tokyo, but staff may not know what's in the dashi or the sauces. 肉なし (no meat) doesn't cover dashi: list what you avoid, one ingredient at a time. Naming the ingredients works better than any single word.