Not necessary.

情况：现在的offer letter上面写的是

senior analyst, market research

实际的工作内容是economic and financial analysis of real estate markets

将来绿卡adjust status的时候我的工作可能已经换了，变成financial analyst.

律师跟我讲她准备LCA和绿卡申请的文件中都按照financial analyst走，因为法律上应该按照工作内容去describe job title.  

-LCA is for H1 petition which is for temporary worker. PERM is for I-140 filing which is for permanent worker. So, they are different. When you apply for green card in the future, your employer needs advertize a new permanent position again and then, do the recruitment procedure again. So, your current position/job title and responsibilities does not need to be the same as that of your future position for PERM (green card).