We use the Jenkins build name as a way to communicate the software version that is built and the description for additional information. In the past (before the tables to div conversion?) this caused the rows of the build history widget to sometimes overflow but the names were not truncated an thus readable.

Now however the job name overflow is invisible and thus the history widget unusable (see screenshot, I used the web inspector to sel a long job name on https://ci.jenkins.io for the screenshot - the issue in our live jenkins looks identical)

A few examples of job names we use:
21.4.5
21.4.5.135
21.4.5.2-git1234567
21.4.5.2-name-of-the-feature-branch-possibly-long.buildnr
vm-hostnames (which usually share a common prefix that is almost too long already)

Job descriptions are usually also used to communicate additional information and thus can't hold the version information.

The Jenkins build number is only ever visible in our Jenkins if a build failed too early to set an interesting job name.