Is the term "Quantum GIS" trademarked?
The phrase, "Quantum GIS", is not found in the US Trademark electronic search.
Trademark status is not mentioned on the Quantum GIS website, nor is,
a trademark symbol nor statement used in the documentation.
The OSGeo website does have two trademark-related pages, but they only mention various OSGeo and FOSS trademarks.
You might check the archives of the mailing lists, particularly the project steering committee.
Their wiki discusses how to cite the software
Cite the QGIS project in general
Quantum GIS Development Team, <YEAR>. Quantum GIS Geographic Information System. Open Source Geospatial Foundation Project. http://qgis.osgeo.org
Yes, QGIS is now trademarked, see https://www.qgis.org/en/site/getinvolved/governance/trademark/index.html for more details.
Previous answer
Short answer: No it is not yet trademarked.