Self-aware, with a hyphen. I wouldn't recommend checking Google when in doubt about a spelling. Check a dictionary. They're much more reliable.
How do you write self-aware?
7 Ways to Increase Self-Awareness in Writing
- Mindfulness training. Being mindful means being completely present in the now and seeing things are they are, rather than seeing them the way you want to see them. ...
- Practice yoga. ...
- Journaling. ...
- Psychotherapy. ...
- Creative Visualization. ...
- Meditation. ...
- Hypnosis.
Is self Service always hyphenated?
Self. The prefix self is always hyphenated: self-made, self-addressed, self-sustaining, etc.