The present paper is further development of our previous publication about revealing false usernames of accounts as a result of hackers' attacks. Although both papers use methods for machine learning analysis, the novelty in this publication consists in applying the quantum technique for making cluster analysis and a new chaotic generator producing fake usernames with unfixed length. The consequence of actions necessary for analyzing the names of users' accounts is following. First, a chaotic pseudo random number generator (PRNG) producing aperiodic time series is proposed. Following given rules, the latter are used to produce fake accounts usernames used as a data base to test the efficiency in avoiding malicious intentions. The generated names are with low, middle and high randomization. Second, these names feed as an input to the quantum machine learning algorithm, which divides them in different clusters. Next, the Quantum Silhouette algorithm for quality evaluation of the results from clusterization, is applied. In the end of the paper, the suggested new technique-chaotic generator and quantum clustering algorithm-is illustrated on the illustrative example including 100 000 usernames of accounts. Keywords-chaotic pseudo random number generator (PRNG), quantum machine learning clustering, k-means, Silhouette