This request has been made many times. It has not yet been implemented because the change would be costly to make due to internal use of the connection name through the GeoWorkspace and Library. - Hal
I agree with Hal that this change would be costly but also it has been done by the ebMap Publisher Command which renames all the connections, so ... the code exists.
We plan to include this with GeoMedia 16.6, currently targeting Oct 2019.
Delivered with the GeoMedia Desktop 2020 release.