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\SetAlgorithmName changes the prefix that comes in caption with \begin{algorithm}...\caption{lol...}\end{algorithm} from \usepackage{algorithm2e}.

But how to change that prefix/name for functions? Procedures? Etc? Is there \SetFunctionName?

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There exist

\SetAlgoProcName{a name}{an autoref name}
\SetAlgoFuncName{a name}{an autoref name}

see the user manual of algorithm2e v5.2, sec. 6, page 17 (near the end of that page).

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