Date without year

Edit: there is an undocumented showyear key. You can apply this for a single language using for example \DTMsetbool{en-GB}{showyear}{false} or for all languages using \DTMlangsetup{showyear=false}. The second version issues a warning because the key is not applicable to some regions in the hierarchy, such as english-base. This warning can be suppressed using \DTMlangsetup* (see datetime2 -- Warnings when using showyear setting).

This setting changes the behavior of \DTMDisplaydate throughout the document, but you can reset it after use.

MWE:

\documentclass{scrbook}
\usepackage[english,main=british]{babel}
\usepackage[useregional]{datetime2}

\begin{document}

\DTMlangsetup*{showyear=false}
\DTMDisplaydate{2020}{2}{10}{-1} is the date

\DTMlangsetup*{showyear=true}
\DTMDisplaydate{2020}{2}{10}{-1} is the date

\end{document}

Result:

---

Original answer:

You can define a new date format without year, as described in the manual (e.g., page 96 and further).

When you want to use the new format you need to set it using \DTMsetdatestyle which will affect \DTMDisplaydate. It does not seem possible to set it just for single use, so afterwards you need to reset the style to what it was before, in the MWE this is en-GB (because of main=british). Note that you need to add the calc package option for datetime2 to use the \DTMmonthname macro.

MWE:

\documentclass{scrbook}
\usepackage[english,main=british]{babel}
\usepackage[useregional,calc]{datetime2}

\begin{document}

\DTMnewdatestyle{noyear}{%
\renewcommand{\DTMdisplaydate}[4]{%
\DTMenglishordinal{##3} \DTMmonthname{##2}}%
}
\DTMsetdatestyle{noyear}
\DTMDisplaydate{2020}{2}{10}{-1}

\DTMsetdatestyle{en-GB}
\DTMDisplaydate{2020}{2}{10}{-1}

\end{document}

Result:

Note that the redefinition includes \DTMenglishordinal in order to keep the ordinal (th) from being printed as superscript. A more international version is \ordinalnum from the fmtcount package (which supports a number of European languages) but only as superscript as far as I know.

I introduce \stripyear to help.

\documentclass{scrbook}
\usepackage[english,main=british]{babel}
\usepackage[useregional]{datetime2}
\newcommand\stripyear[1]{%
  \edef\tmp{#1}\expandafter\stripyearaux\tmp\relax}
\def\stripyearaux#1 #2 #3\relax{#1 #2}
\begin{document}
\stripyear{\DTMDisplaydate{2020}{2}{10}{-1}}.
\end{document}