sudo update-alternatives --config java
update-alternatives: error: no alternatives for java

The installed java versions need to be added to update-alternatives:

adding jdk-11 with 10 priority :

sudo update-alternatives --install /usr/bin/java java /usr/lib/jvm/java-11-openjdk-amd64/bin/java 10 

adding jdk-15 with 20 priority (suppose you have extracted the tarball to /usr/lib/jvm/ directory. In your case replace /usr/lib/jvm/jdk-15.0.2/bin/java with /usr/local/bin/jdk-15.0.2/bin/java)

sudo update-alternatives --install /usr/bin/java java /usr/lib/jvm/jdk-15.0.2/bin/java 20

Check it:

 sudo update-alternatives --list java

/usr/lib/jvm/java-11-openjdk-amd64/bin/java
/usr/lib/jvm/jdk-15.0.2/bin/java

and

sudo update-alternatives --config java

sample output:

There are 2 choices for the alternative java (providing /usr/bin/java).

  Selection    Path                                         Priority   Status
------------------------------------------------------------
* 0            /usr/lib/jvm/jdk-15.0.2/bin/java              20        auto mode
  1            /usr/lib/jvm/java-11-openjdk-amd64/bin/java   10        manual mode
  2            /usr/lib/jvm/jdk-15.0.2/bin/java              20        manual mode

Press <enter> to keep the current choice[*], or type selection number: 

Check the java version, in the above example the default version is jdk-15:

java --version

openjdk 15.0.2 2021-01-19
OpenJDK Runtime Environment (build 15.0.2+7-27)
OpenJDK 64-Bit Server VM (build 15.0.2+7-27, mixed mode, sharing)

Alternatively, you can use adoptopenjdk repository:

wget -qO - https://adoptopenjdk.jfrog.io/adoptopenjdk/api/gpg/key/public | sudo apt-key add -

sudo add-apt-repository --yes https://adoptopenjdk.jfrog.io/adoptopenjdk/deb/

sudo apt-get update && sudo apt-get install adoptopenjdk-8-hotspot

https://adoptopenjdk.net/installation.html