No. The Eleventh Doctor told Craig Owens that he was the "Eleventh" after they bumped heads in "The Lodger". The incarnation who followed the Eighth Doctor & who fought in the Time War didn't use the name Doctor (although he's referred to as the "War Doctor" in screen credits &c). The next incarnation resumed using the name Doctor & was therefore the Ninth Doctor, even though he was the tenth incarnation. Ten's aborted regeneration in "Journey's End" does count as a regeneration used but he remained the same incarnation (in "The Time of the Doctor", Eleven said he had vanity issues at the time). Thus, the Eleventh Doctor is the Eleventh Doctor but is the twefth incarnation & has used twelve regenerations.