you need to create a .desktop file for it and set StartupWMClass in that to whatever the app uses.

st-new-desktopentry-0.8.2-with-startupwmclass.diff

From 0ba2850930d2ef22a1774f3dc78884c978f2d8be Mon Sep 17 00:00:00 2001
From: aleks <aleks.stier@icloud.com>
Date: Wed, 27 May 2020 01:20:00 +0200
Subject: [PATCH] Create a desktop-entry for st

---
 Makefile   | 3 +++
 st.desktop | 7 +++++++
 2 files changed, 11 insertions(+)
 create mode 100644 st.desktop

diff --git a/Makefile b/Makefile
index ed19e70..29e25b9 100644
--- a/Makefile
+++ b/Makefile
@@ -50,9 +50,12 @@ install: st
 	chmod 644 $(DESTDIR)$(MANPREFIX)/man1/st.1
 	tic -sx st.info
 	@echo Please see the README file regarding the terminfo entry of st.
+	mkdir -p $(DESTDIR)$(PREFIX)/share/applications
+	cp -f st.desktop $(DESTDIR)$(PREFIX)/share/applications
 
 uninstall:
 	rm -f $(DESTDIR)$(PREFIX)/bin/st
 	rm -f $(DESTDIR)$(MANPREFIX)/man1/st.1
+	rm -f $(DESTDIR)$(PREFIX)/share/applications/st.desktop
 
 .PHONY: all options clean dist install uninstall
diff --git a/st.desktop b/st.desktop
new file mode 100644
index 0000000..a1b5116
--- /dev/null
+++ b/st.desktop
@@ -0,0 +1,7 @@
+[Desktop Entry]
+Version=1.0
+Name=st
+Comment=Fast and simple terminal emulator
+Type=Application
+Icon=utilities-terminal
+Exec=st
+Categories=Utility;TerminalEmulator;X-Suckless;
+StartupWMClass=st-256color
+GenericName=Simple Terminal
+Terminal=false
+StartupNotify=false
-- 
2.26.2