How to make Bash completion work with non-standard command name, e.g. "tg" instead of "terragrunt"?

[heidemn-faro]

No matter if tg is a symlink or a regular file, this doesn't work:
complete -C $HOME/.local/bin/tg tg

For some reason, it successfully completes options:
$ tg -<TAB>
...but doesn't complete commands:
$ tg <TAB>

The same is working fine with terraform & my tf symlink.
Here it completes both commands and options.

My .bashrc:

complete -C /usr/local/bin/terragrunt terragrunt
complete -C $HOME/.local/bin/tg tg

complete -C /usr/local/bin/terraform terraform
complete -C $HOME/.local/bin/tf tf

Versions:

$ cat /etc/os-release  | grep PRETTY
PRETTY_NAME="Ubuntu 22.04.5 LTS" ## in WSL2, Win11

$ bash --version
GNU bash, version 5.1.16(1)-release (x86_64-pc-linux-gnu)

$ tf version
Terraform v1.11.4
on linux_amd64

$ tg version
terragrunt version v0.93.8

Does someone have an idea how to solve this?
Thanks :-)