You can build an image with several tags and then push the image with the --all-tags option.
Example:
docker build -t reg/user/image:foo -t reg/user/image:latest .
docker push reg/user/image --all-tags
Older Docker clients that do not support --all-tags will push all tags by default (simply omit the option), newer clients will only push latest by default. As an alternative, you may want to push each tag separately.