Global models are trained to be as generalizable as possible, with user invariance considered desirable since the models are shared across multitudes of users. As such, these models are often unable to produce personalized responses for individual users, based on their data. Contrary to widely-used personalization techniques based on few-shot learning, we propose UserIdentifier, a novel scheme for training a single shared model for all users. Our approach produces personalized responses by adding fixed, non-trainable user identifiers to the input data. We empirically demonstrate that this proposed method outperforms the prefix-tuning based state-of-the-art approach by up to 13%, on a suite of sentiment analysis datasets. We also show that, unlike prior work, this method needs neither any additional model parameters nor any extra rounds of few-shot fine-tuning.