Text-embedding models often exhibit biases arising from the data on which they are trained. In this paper, we examine a hitherto unexplored bias in text-embeddings: bias arising from the presence of names such as persons, locations, organizations etc. in the text. Our study shows how the presence of name-bias in text-embedding models can potentially lead to erroneous conclusions in the assessment of thematic similarity. Text-embeddings can mistakenly indicate similarity between texts based on names in the text, even when their actual semantic content has no similarity or indicate dissimilarity simply because of the names in the text even when the texts match semantically. We first demonstrate the presence of name bias in different text-embedding models and then propose text-anonymization during inference which involves removing references to names, while preserving the core theme of the text. The efficacy of the anonymization approach is demonstrated on three downstream NLP tasks involving embedding similarities, achieving significant performance gains. Our simple and training-optimization-free approach offers a practical and easily implementable solution to mitigate name bias.