.(החדש הזה לכם ראש חדשים ראשון הוא לכם לחדשי השנה” (שמות י”ב,ב“
The month the Jewish people left Mitzrayim is to be counted as the first month of the year. The Ramban explains that the purpose of counting this way is to remember יציאת מצרים. On every occasion that we mention the months the miracle will be recalled. For this reason the months have no names in the Torah, rather it says in the third month, in the second month etc. When we left Bavel however, we started using the Babylonian names of the months, Nissan, Iyur etc. to remember that Hashem took us out of Bavel. There is a big debate amongst the Poskim if it is permitted to count by the secular months and year.
The author of the עין יעקב in his commentary הכותב writes there is no prohibition to mention the secular names of the months; for example March and April. There is a prohibition however to count by the secular months. A person should not say April is the fourth month. By doing so, he will be transgressing the mitzvah of החדש הזה לכם ראש חדשים. Others say that it is still better to abbreviate the name of the months, for some of them [January and March] are the names of gods.
The מהר”ם שיק is of the opinion that there is also a Torah prohibition to count by the secular year. This prohibition falls under the category of “שם אלהים אחרים לא תזכירו” – do not mention the names of other gods. By counting the secular year we are remembering their god. Some say it is not a problem because according to the הגהות מיימוניות and theדרכי משה in יורה דעה סימן קמ”ז it is only prohibited if the name of the god is mentioned to show power and godliness.
The בנין שלמה says that there is no issur nowadays to count the secular month. The mitzvah to count the year from Nissan only applies when the mitzvah of kiddush hachodesh was performed. Not at any different time. Accordingly there should be no issue with writing or using the secular month. When required for business purposes one may write or mention the name of the secular month as the first month.
הג”ר משה שטרנבך שליט”א says an additional heter to write the non-Jewish month, because the non-Jews use a solar calendar while we use a lunar calendar. Therefore when one is writing the secular month, one is not counting the Jewish months with a different name, so there is no issue. The issue of counting Nissan as the first month only applies when we count according to the moon, not according to the sun.
The חתם סופר in this week’s parsha writes that one should not ח”ו count the months or the years according to the secular calendar. At the same time however the חתם סופר himself writes in his teshuvos the secular year? הג”ר נתן געשטעטנער זצ”ל explains that those teshuvos pertained to matters that were relevant to dealings with non-Jews. Without mentioning the secular year it would be difficult to know the exact date. Even though as a result the avodah zarah may be mentioned, the Rishonim say that it is permitted since the purpose of mentioning it is to teach a halacha.
The מנהג העולם is that most are not careful in writing the months or the year of the secular calendar. The פרדס יוסף explains the מנהג with the ruling of the ספר העיקרים who says that the mitzvah to count the months with the first month as ניסן was nullified by ירמיהו הנביא. It says in the passuk “ולא יאמר עוד חי ה’ אשר העלה את בני ישראל מארץ מצרים כי אם חי ה’ אשר העלה את בני ישראל מארץ צפון ומכל הארצות אשר הדחתים שמה והשבתים על אדמתם אשר נתתי לאבותם” (ירמיה ט”ז,י”ד-ט”ו). This is referring to the final גאולה. The ספר העיקרים holds that since that נבואה, there is no longer a mitzvah to count the months from יציאת מצרים. In fact they started counting the Babylonian months when they left Bavel.
As for the secular year many poskim are lenient since there is no mention in שלחן ערוך of a prohibition to think about avodah zarah without saying the name. Additionally the יביע אומר says it is not clear whether non-Jews count their years from yoshka’s birth or not. Rather this is a simple number that is accepted by everyone.
Reb Moshe Feinstein zt”l was lenient with writing the secular date on a check. Reb Yaakov Kamenetsky and the Satmar Rav zt”l were stringent.
Many people are careful to only write the last two numbers of the year and not the complete year. Others are careful when they write the secular year to also write למספרם – according to their counting, to show that we count differently.
The אבני ישפה says that although there are heterim one should still realize that we should be separate from the non-Jews and not use the secular date when it is not necessary. 
Prepared by R’ Avrohom Yehoshua Ziskind
 In reality the secular months are mostly not names of avodah zarah of any sort. May, June, July, and August are names of Kings. Other months are simply numbers. For example, December is ten in Latin, November is nine, October is eight, and September is seven. February means purification and April is the time of growth.
 Many other Poskim over the years wrote the secular date on their response such as the מהר”ם פאדוה, חות יאיר רמ”א.
 Sources: Halachically Speaking,אוצר פלאות התורה,פסקי תשובות