G-ERTI is the plane at the centre of MJN Air. It can provide seating for 16 passengers plus cabin crew. It is a Lockheed McDonnel 3-12 (a fictional aircraft), and is past its best. 'It's only gaffer tape and hope holding it together'. Some of its faults include faulty lights (not all the non-smoking lights turn off and on, and there's one that can't be turned on because it makes the cabin smell of fish).
Gerti is so-called because it is the registration of the aircraft, G-ERTI.
The full callsign (Golf Echo Romeo Tango India, phonetic for the registration, G-ERTI) must be said when joining a new ATC region, or in the case of an emergency. At other times, it may be shortened (which is why it is sometimes heard as being Golf Tango India).
G-ERTI is MJN’s only aircraft, which is the most likely reason for the registration also being the callsign. Bigger airlines (i.e.actual airlines) usually use their airline name or some other identifying word as their callsign, often alongside a number - British Airways are Speedbird, South African Airways are Springbok, and QANTAS are, wait for it, QANTAS.
In general aviation, the aircraft registration doubles as the call sign. MJN’s callsign (although a company; civil not general aviation) is probably their registration because they are not technically an airline. They barely even qualify as a functional company most of the time. They only have one jet. They could (legally) go by their company name (some airlines do, Monarch Airlines and QANTAS are examples), but G-ERTI being called MJN-1 would make absolutely no sense and implies that they are a functional airline with at least two jets. Which they are most certainly not. 
There appears to be an alarmingly large number of mechanical problems with the dilapidated aircraft, and it's considered a miracle that she still actually flies. When Linda remarks that she didn't think there were any Lockheed McDonnell 3-12s still flying, Douglas remarks "...those there are, barely do" (Newcastle).
G-ERTI is, however, surprisingly valuable; it is discovered that G-ERTI's wiring is made entirely from gold, rather than the more usual copper. This is revealed to be a scheme by Gordon Shappey, the previous owner, to allow him to evade losses in his divorce settlement with Carolyn; hence, when she is unexpectedly awarded the jet in the settlement, his incessant attempts to buy her back from Carolyn, even at a very high price. This discovery allows MJN to continue functioning (renamed, though, as OJS- 'Our Jet Still') and proves to be the reason for G-ERTI's extreme sluggishness in the air.
The registration G-ERTI is, in real life, allocated to a Staaken Z-21A Flitzer.