The page https://confluence.atlassian.com/display/BAMBOO/Variables+for+deployment+environments list available release variables.

${bamboo.deploy.version}
${bamboo.deploy.version.previous}

This returns the name of the release. The following also returns same:

${bamboo.deploy.release}
${bamboo.deploy.release.previous}

It will be nice to mention that either will work or replace the keywords version with release.