Marcheline (MARSH-el-een) is French, meaning "warlike" or "little warrior." It is the French feminine variant of Marcel, which comes from the Roman god of war, Mars. It is also the name of Marcheline Bertrand (birth name Marcia Lynne), Angelina Jolie's mother, and the middle name of her daughter Vivienne.
I selected Marcheline for March because March would make a super cute nickname. Chella, Marla, Marly, Marline, and Shelly could also work. In the past decade or more there were no baby girls named Marcheline, but that is not the case for Marchella, only given since about 1956 and last seen on 5 baby girls in 2012 (and never given to more than 11 in a year) and Marchelle, which peaked in 1963 with 64 births and was last seen in 2013 on 6 girls. Marcelle, which has little difference in sound from the masculine Marcel, is doing well in France but was only given to 8 girls in the U.S. in 2015. The spelling Marcela ranked in 1991, 1992 and 1999, while Marcella ranked from 1900 until 2002, only missing a few years in between. Streamlined Marceline peaked in 1928 and is definitely back on the rise, jumping from only 6 girls given the name in 2010 to suddenly 143 in 2014. Feminissima Marcelina has gone from nonexistent in the 1880's to being used 33 times in 2015. Italian Marciana (mar-CHA-nah), used since the 1920's, finally peaked in 2009 with 14 girls given the name. Marcia fares better than all of the above, its height in 1951 when given to 5,299 baby girls.