I used these commands in order to have along with the \mathcal{L} a calligraphic L as well
\documentclass[11pt,a4paper]{report}
\usepackage{amsmath,amssymb}
\usepackage{calrsfs}
\DeclareMathAlphabet{\pazocal}{OMS}{zplm}{m}{n}
\newcommand{\La}{\mathcal{L}}
\newcommand{\Lb}{\pazocal{L}}
\begin{document}
$\La \Lb$
\end{document}
but now the other letters with \mathcal are not what they supposed to be. My question is, therefore, how can I keep using the \La,\Lb commands for the two L's and at the same time have the usual output of \mathcal for other letters, take \mathcal{O} for example.

\documentclass. Since font selection is affected greatly by the class, that will give potential helpers a realistic example that they can experiment with. – barbara beeton Sep 21 '19 at 17:52\mathcaland the other as\mathscrwith themathallphapackage. – Davislor Sep 22 '19 at 08:12\usepackage{calrsfs}with another math alphabet definition, similar to the one you used for\pazocal. Be aware that you have only a limited number of math alphabets, unless you switch tounicode-math. – Davislor Sep 22 '19 at 08:15