It's possible for 'generate a prefix' algorithm to generate a prefix conflicting with an existing one

https://w3c.github.io/DOM-Parsing/#generating-namespace-prefixes

The algorithm just generates 'ns1', 'ns2', ... without checking existence of generated prefixes.
So, the following example serializes two xmlns:ns1 on child element if we follow the current specification. WPT domparsing/XMLSerializer-serializeToString.html already has a test case ("Check if "ns1" is generated even if the element already has xmlns:ns1.").

const root = (new DOMParser()).parseFromString('<root xmlns:ns2="uri2"><child xmlns:ns1="uri1" xmlns:a0="uri1" xmlns:NS1="uri1"/></root>', 'text/xml').documentElement;
root.firstChild.setAttributeNS('uri3', 'attr1', 'value1');
console.log((new XMLSerializer()).serializeToString(root));

The algorithm should have a loop until a generated prefix is not found.

Start with the generating namespace prefixes algorithm in the linked DOM-Parsing specification and review WPT domparsing/XMLSerializer-serializeToString.html, including the existing ns1 test. Done means generated prefixes are checked with the specification’s “found” condition so serialization does not create a conflicting duplicate prefix.