Party leader Göran Hägglund is reported to be lukewarm to the idea, which was discussed at the most recent meeting of the party executive.
The Christian Democrats have declined from an 11.7 percent high in the 1998 general election to 5.6 percent in September 2010, which renders it the smallest parliamentary party, together with the Left Party.
The party faithful and hierarchy are busy analysing the dire election result and one of the suggestions that has emerged, is the possibility of a name change to rebrand the party.
Aside from the "family party", other alternatives under consideration include the "freedom party" as additions to the current name, pointing out that other parties - such as the Liberals and the Social Democrats - have extended names.
Some members of the executive are in favour of doing away with the name Christian Democrats altogether in order to try to broaden the party's appeal, the newspaper reported.
The party's youth wing chair, Charlie Weimers, confirmed to SvD that the executive had discussed the issue at a recent meeting.
Party leader Göran Hägglund is reported to be less enthusiastic about the move, but welcomes the discussion and is prepared to consider all alternatives to arrest the slide.