Does consistency in how my name is presented/abbreviated as author on a publication matter? Assume I have the name: "First Middle Last". I have been publishing as "First Last." 

At my current job (postdoc) my adviser prefers that I list my name on my paper as F. Last (or F.M. Last), and I'm afraid that the change in style will make it less obvious that all the papers I've written are from the same person. Is this an issue that matters? If so, does it matter enough to insist on using "First Last" in spite of all other names being abbreviated on any papers?

P.S. If this is a community dependent question, I'm a physicist in the AMO physics and optics communities (e.g. APS and OSA).  I'm asking about how my name appears in the list of authors on the paper I wrote (not about how citations are formatted).
If you find yourself publishing under multiple names, e.g., "First Last" in one journal and "F. Last" in another, you might want to consider registering for an ORCiD. ORCiD provides a unique identifier which a researcher can use to unite all the different names she/he has published under. 

If you have a more common name, like "John Smith", an ORCiD can help differentiate you from other researchers with similar names. And if you change your name, ORCiD can help you link the older to the newer.