I could find any sources.
How many galaxies are counted, named and mapped?
How many more there are to be mapped in the future(the total count)?
Are there galaxies in the observable universe that are too far away to be detected?
How many databases exist with the list of universe objects(are there more than one concurrent projects)?
Here's a partial answer. I hope it helps.
Are there galaxies in the observable universe that are too far away to be detected?
Yes and no. By definition, all the objects in the observable universe can be detected. However, the observable universe does not encompass the entire universe (we think!), and so there are probably many more galaxies out there. Some outside the observable universe are receding faster than the speed of light, and therefore can never be detected.
How many more there are to be mapped in the future(the total count)?
You can't really count a number of objects if you don't know how many there are. However, I've found estimates of 170 billion and 125 billion; the latter is backed up here, which also includes a question that says that the number could supposedly be a staggering 500 billion (although no sources are given). We don't know for sure. This gives a range of 100-200 billion; this agrees; this says 100 billion; this says 500 billion. I'd go for a figure in the mid-100 billions, based on these claims.
I can't (at the moment) find reasonable data for your other two questions, but I'll update this answer if I can.
