No, there is no supported way to rename your core server.
Easier might be to install a new server and point to your existing DB. That way you will keep everything, besides shares and such that you might need to re-create.
Frank, ive tried to do this but som e features like Alerting, VulnerabilityData, etc. get from database the old core server name.
On the database, there are several tables with column SourceCore/Hostname that i guess that is used by LDMS to provide URL's to console get it.