For publications, what do I do when my first name is abbreviated? I'm Muslim, I use Md. as for Muhammad. So when submiting to journals, should I stick to the 2nd &amp; 3rd names? I'm currently facing problems in submitting to arxiv.org which asks for only first and last names.
This shouldn't really be a problem these days in most places, because the entry fields on most web-based entry forms are smart enough to recognize and accept spaces. Thus, even when the site asks for a first name only, you can put in "Md. [Middle Name]" as your first name.

As Dave suggests in the comment, unless you have a really uncommon last name—one that doesn't show up in ISI or arXiv.org searches at all right now, you're better off having parts of three names show up. It's also helpful to keep your professional name fixed throughout your career. (In other words, if you want to go by Md. [Middle] [Last], use that same form whenever possible.)