By Steve Holland MANCHESTER, New Hampshire (Reuters) -U.S. President Joe Biden won an unusual Democratic write-in vote in New Hampshire’s primary election on Tuesday, an important display of political strength, despite his name not being on the ballot. Edison Research projected Biden the winner over two Democrats whose names were actually on the ballot – U.S. Representative Dean Phillips of Minnesota and self-help author Marianne Williamson. The victory for the incumbent president was the end product of a fervent write-in campaign orchestrated by New Hampshire Democrats, who were troubled by t…