EMB500 Captain experiences difficulty locating ELVAE intersection after being cleared direct during the RUUDY2 RNAV from TEB. Although the RNAV SID was presented on the MFD; the SID chart was not readily available.

Narrative

Cleared to ELVAY Intersection; we were climbing from 2;000 FT to 4;000 FT with Captain (me) at the controls. Pilot not flying did not understand intersection (ELVAY). I heard it and repeated it back to ATC. Neither of us has ever heard of this intersection. We should have. I briefed SID in depth and so did pilot not flying or so we thought. I briefed possible intersections but did not see ELVAY. We did not have plate out but map was up on screen. I clicked 'nearest' and 'intersections.' Nothing; I can't find it. The new frequency [we were on was] very; very busy. Now we are still on heading approximately 30 seconds pass. We go back to other frequency. He asks while I grab chart I see ELVAY; program and fly to it. ATC gave us heading before I could load after our query. No conflicts. I realize now that even though we have sophisticated cockpit with MFD; keep the darn plate out. I should brief all possible intersections and I did. Well; I better slow down and double check. I think I fly into TEB so much I have heard all intersections and this revision was a couple of years old; so it was not new. I also realized that if I scrolled to page 2 on nearest intersection page; it was there. We have been designing a new checklist for this aircraft to be approved by FAA. I have noticed how much improvement I have seen and I was proud of our progress. Well; I now realize that briefing an 'old hat' airport is maybe more important than new one because of confidence factor. I should have seen this intersection and briefed it as well. What makes me mad is that I always say no rush as we brief/prepare so that no crewmember will feel rushed in anyway. A CRM process I am aware of and want to establish calm/non-rushed cockpit.