Fixed in copyartifact-1.35.1.
It will be available in a day.

You also need to upgrade your Jenkins to 1.580.1 or later.

Code changed in jenkins
User: ikedam
Path:
src/main/java/hudson/plugins/copyartifact/CopyArtifact.java
http://jenkins-ci.org/commit/copyartifact-plugin/b2ccc3959246aa17b8e3565441be70335a7ad4e5
Log:
Merge pull request #64 from ikedam/feature/JENKINS-27475_AvoidsNpeForUnexpectedCase

JENKINS-27475 Avoids NPE on renaming a project.

Compare: https://github.com/jenkinsci/copyartifact-plugin/compare/406248600e3b...b2ccc3959246

Code changed in jenkins
User: ikedam
Path:
src/main/java/hudson/plugins/copyartifact/CopyArtifact.java
http://jenkins-ci.org/commit/copyartifact-plugin/f71ab1230f153397f4bd6e1412b59c4f04d6e02b
Log:
[FIXED JENKINS-27475] Avoids NPE on renaming a project though it's unclear why this happens.

https://github.com/jenkinsci/copyartifact-plugin/pull/64

As far as I know, configurations causing this problem cannot not be created with project configuration pages.
I'm not sure how such incomplete configuration is created.

Anyway, avoiding this is very easy, and I plan to fix this in the next release.
Latest copyartifact is targeted to Jenkins > 1.580.1 and you will need to upgrade Jenkins to install copyartifact with that fix.

Thanks Daniel for sharing workaround.but it did not work.
after entry the missed "project Name" in field at copy artifacts build step at all found projects, still below issue appeared.

javax.servlet.ServletException: java.lang.NullPointerException
at org.kohsuke.stapler.Stapler.tryInvoke(Stapler.java:778)
at org.kohsuke.stapler.Stapler.invoke(Stapler.java:858)
at org.kohsuke.stapler.MetaClass$6.doDispatch(MetaClass.java:248)
at org.kohsuke.stapler.NameBasedDispatcher.dispatch(NameBasedDispatcher.java:53)
at org.kohsuke.stapler.Stapler.tryInvoke(Stapler.java:728)
at org.kohsuke.stapler.Stapler.invoke(Stapler.java:858)
at org.kohsuke.stapler.Stapler.invoke(Stapler.java:631)
at org.kohsuke.stapler.Stapler.service(Stapler.java:225)
at javax.servlet.http.HttpServlet.service(HttpServlet.java:717)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:290)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:206)
at hudson.util.PluginServletFilter$1.doFilter(PluginServletFilter.java:96)
at com.cisco.step.jenkins.plugins.people.redirector.PeopleRedirectorPlugin$1.doFilter(PeopleRedirectorPlugin.java:91)
at hudson.util.PluginServletFilter$1.doFilter(PluginServletFilter.java:99)
at hudson.plugins.greenballs.GreenBallFilter.doFilter(GreenBallFilter.java:58)
at hudson.util.PluginServletFilter$1.doFilter(PluginServletFilter.java:99)
at hudson.util.PluginServletFilter.doFilter(PluginServletFilter.java:88)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:235)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:206)
at hudson.security.csrf.CrumbFilter.doFilter(CrumbFilter.java:48)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:235)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:206)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:84)
at hudson.security.UnwrapSecurityExceptionFilter.doFilter(UnwrapSecurityExceptionFilter.java:51)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at jenkins.security.ExceptionTranslationFilter.doFilter(ExceptionTranslationFilter.java:117)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at org.acegisecurity.providers.anonymous.AnonymousProcessingFilter.doFilter(AnonymousProcessingFilter.java:125)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at org.acegisecurity.ui.rememberme.RememberMeProcessingFilter.doFilter(RememberMeProcessingFilter.java:142)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at org.acegisecurity.ui.AbstractProcessingFilter.doFilter(AbstractProcessingFilter.java:271)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at org.acegisecurity.ui.basicauth.BasicProcessingFilter.doFilter(BasicProcessingFilter.java:174)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at jenkins.security.ApiTokenFilter.doFilter(ApiTokenFilter.java:79)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at org.acegisecurity.context.HttpSessionContextIntegrationFilter.doFilter(HttpSessionContextIntegrationFilter.java:249)
at hudson.security.HttpSessionContextIntegrationFilter2.doFilter(HttpSessionContextIntegrationFilter2.java:67)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at hudson.security.ChainedServletFilter.doFilter(ChainedServletFilter.java:76)
at hudson.security.HudsonFilter.doFilter(HudsonFilter.java:164)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:235)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:206)
at org.kohsuke.stapler.compression.CompressionFilter.doFilter(CompressionFilter.java:46)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:235)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:206)
at hudson.util.CharacterEncodingFilter.doFilter(CharacterEncodingFilter.java:81)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:235)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:206)
at org.apache.catalina.core.StandardWrapperValve.invoke(StandardWrapperValve.java:233)
at org.apache.catalina.core.StandardContextValve.invoke(StandardContextValve.java:191)
at org.apache.catalina.authenticator.AuthenticatorBase.invoke(AuthenticatorBase.java:470)
at org.apache.catalina.core.StandardHostValve.invoke(StandardHostValve.java:127)
at org.apache.catalina.valves.ErrorReportValve.invoke(ErrorReportValve.java:102)
at org.apache.catalina.core.StandardEngineValve.invoke(StandardEngineValve.java:109)
at org.apache.catalina.connector.CoyoteAdapter.service(CoyoteAdapter.java:298)
at org.apache.coyote.http11.Http11Processor.process(Http11Processor.java:857)
at org.apache.coyote.http11.Http11Protocol$Http11ConnectionHandler.process(Http11Protocol.java:588)
at org.apache.tomcat.util.net.JIoEndpoint$Worker.run(JIoEndpoint.java:489)
at java.lang.Thread.run(Thread.java:744)
Caused by: java.lang.NullPointerException
at hudson.plugins.copyartifact.CopyArtifact$ListenerImpl.onRenamed(CopyArtifact.java:466)
at hudson.model.listeners.ItemListener.fireLocationChange(ItemListener.java:195)
at hudson.model.AbstractItem.renameTo(AbstractItem.java:298)
at hudson.model.Job.renameTo(Job.java:611)
at hudson.model.Job.doDoRename(Job.java:1385)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:57)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
at java.lang.reflect.Method.invoke(Method.java:606)
at org.kohsuke.stapler.Function$InstanceFunction.invoke(Function.java:298)
at org.kohsuke.stapler.interceptor.RequirePOST$Processor.invoke(RequirePOST.java:46)
at org.kohsuke.stapler.Function$InterceptedFunction.invoke(Function.java:399)
at org.kohsuke.stapler.Function.bindAndInvoke(Function.java:161)
at org.kohsuke.stapler.Function.bindAndInvokeAndServeResponse(Function.java:96)
at org.kohsuke.stapler.MetaClass$1.doDispatch(MetaClass.java:120)
at org.kohsuke.stapler.NameBasedDispatcher.dispatch(NameBasedDispatcher.java:53)
at org.kohsuke.stapler.Stapler.tryInvoke(Stapler.java:728)
... 60 more

It's fairly obvious what happens.

https://github.com/jenkinsci/copyartifact-plugin/blob/master/src/main/java/hudson/plugins/copyartifact/CopyArtifact.java#L546

Copy Artifact cannot deal with incomplete job configurations and assumes every Copy Artifact build step has a project name defined.

Workaround: Find the project in your Jenkins with a Copy Artifact build step and empty "Project Name" form field. Enter a project name.

This is likely unrelated to Job Config History, it just fails to receive all notifications. Difficult to say given the ancient Jenkins version you're using.