Speaker anonymization aims to conceal a speaker's identity while preserving content information in speech. Current mainstream neural-network speaker anonymization systems disentangle speech into prosody-related, content, and speaker representations. The speaker representation is then anonymized by a selection-based speaker anonymizer that uses a mean vector over a set of randomly selected speaker vectors from an external pool of English speakers. However, the resulting anonymized vectors are subject to severe privacy leakage against powerful attackers, reduction in speaker diversity, and language mismatch problems for unseen language speaker anonymization. To generate diverse, language-neutral speaker vectors, this paper proposes an anonymizer based on an orthogonal Householder neural network (OHNN). Specifically, the OHNN acts like a rotation to transform the original speaker vectors into anonymized speaker vectors, which are constrained to follow the distribution over the original speaker vector space. A basic classification loss is introduced to ensure that anonymized speaker vectors from different speakers have unique speaker identities. To further protect speaker identities, an improved classification loss and similarity loss are used to push original-anonymized sample pairs away from each other. Experiments on VoicePrivacy Challenge datasets in English and the AISHELL-3 dataset in Mandarin demonstrate the proposed anonymizer's effectiveness.