Paste your list with one item per line, choose whether to number the output or drop duplicates, then press Shuffle and copy the randomised list.
Yes. It uses a Fisher-Yates shuffle driven by your browser's secure random generator, which is the standard unbiased algorithm — every possible ordering of your list is equally likely.
Yes. Turn on Remove duplicates and identical lines are collapsed to one before shuffling, so a name entered twice cannot take two slots in the result.
No practical limit. Thousands of lines shuffle instantly because everything runs locally in your browser and nothing is uploaded to a server.