I'm afraid the Internet is very weak on sources/meanings of Amharic names. Might I suggest you ask this question by e-mail of someone else bearing your name? Try one (or better, all) of these people, who should not be offended at all by your question:
Solomon Mebratu Solomonm@csd.uwm.edu
Desta Mebratu firstname.lastname@example.org
Madeo Mebratu M.Mebratu@ee.latrobe.edu.au
Ethiopean Embassy to the US email@example.com
Good luck, and if you get your answer, please post on this message board again to tell us what you've found out.