According to Jehovah's Witnesses, how many of the 144 000 have already been identified? Jehovah's Witnesses believe1 that 144 000 of their number are different to the rest in that they will go to heaven, whereas the rest (presumably several million) will live on paradise Earth.

I'm wondering how near to complete they believe that they are now, eg 25%, 50%, 99%? And do they keep records on the 144 000 so that they can answer this exactly?

1 References: TRiG's answer and Wikipedia.
Anointing of the 144,000 began at Pentecost, 33c.e., and continues down through our day.

The scriptures show the angels are holding back the final judgement against wicked humankind until 144,000 individuals from earth are sealed. (Rev 7:1-4).

Being Anointed is not the same as being sealed.

Anointing is the invitation.

Sealing is the stamp of approval from God that the individual proved faithful to his calling.

Those who have been anointed through history have had God bear witness that they are invited to join Jesus to rule as kings &amp; priests over the earth.  God does the final sealing if someone anointed proves faithful to their calling. Since only God knows who has been faithful it is impossible to determine what percentage has been filled. 

(That being said, Jehovah's witnesses are convinced we are living deep in the last days. It would only make sense the number is very close to being filled)

Regarding your question about records kept, every year at the Memorial observance of Christs death (Nisan 14), Jehovah's witnesses in every country around the world gather together to reflect on Jesus sacrifice and obey his command to "keep doing this in remembrance of me".  Bread and wine is passed, But only those anointed actually partake. Attendants globally record the number of those who partake, and those numbers are published annually in the yearbook of Jehovah's witnesses.

(FYI, in 2016, 20,085,142 attendented the Memorial observance globally, while only 18,013 partook).

For further information on this subject please follow the links below:

https://wol.jw.org/en/wol/d/r1/lp-e/2016045#h=13:171-13:663

https://wol.jw.org/en/wol/pc/r1/lp-e/2013844/0/0