- Yes!
- No!
A brief disclaimer: I have not seen the main-source regarding this topic, merely a summary on a website which works with documents of the military-branch from East-Germany, so while I do not doubt that these documents exist, I cannot vouch for this being 100% historically accurate and I let a lot of my interpretation flow into it, since, for example, the exact version of the T-10 is not stated.
[UPDATE]
I have since come into posession of the name of the document which apparently states that East Germany has ordered or trialed the T-10 heavy tank (version unknown, but I would assume T-10M since the document is dated 1957, the same year the T-10M was adopted, and the tank was planned to be introduced in 1959), the document includes 201 pages and is situated within the Freiburg military-archive.
I am currently not in the position to travel to Freiburg to read through these documents, but as soon as I can I will update this post.
Disclaimer over, here is the suggestion:
After the creation of the NVA in 1956, the GDR quite quickly voiced the order, that multiple heavy-tank brigades were to be put into service. This order was executed just as quickly and IS-2’s, that were beforehand fielded to the KVP (Kasernierte Volkspolizei and the predecessor of the NVA), in 1952, were inherited and put into service with the NVA in the same year as it’s creation: 1956.
However, there were mentions during the same time, that a new heavy tank, the T-10, was planned to be adopted from the USSR for GDR use. In the German documents regarding this tank, it is referred to as “Schwerer Panzer X”, or just “Panzer X”, basically being the “Germanized” version of the name T-10 (tank 10) with the German words “Schwerer Panzer”, meaning heavy tank, and the number 10 being a roman numeral.
A total of 121 T-10s were supposedly ordered in 1957. At the same time, 7.000 shells for the main gun of the Panzer X were ordered, with a further 140.000 planned for 1960. There were also plans for driving-lessons (Motorstunden) planned in 1957, for 1960. The new T-10s were to be fielded by 1959 and the remaining IS-2s were to be converted into towing-machines.
All of these ambitions came to a stop, with the realisation, that the heavy-tank as a concept, will not be effective on the battlefields of the cold war, seeing as the new American M60 was able to perforate the T-10 from the front with it’s 105mm cannon, while a heavy tank would be quite slow and it’s now irrelevant armor did not justify the cumbersomeness of the a tank like the T-10, additionally, seeing as the USSR was constructing a new medium tank, the T-62, the GDR ultimately did not go through with the plan of introducing any T-10 into the NVA, and in fact, dropped the heavy tank altogether from their doctrine.
I will still suggest this vehicle for the German tech-tree, simply because of two reasons: Germany is in need of a replacement for the Tiger II 10,5cm (there really isn’t any other heavy-tank at rank V Germany could get) and, in case a newer version like the T-10B or T-10M is chosen, it could be the only chance for Germany to get a “high-tier” heavy tank.
Specifications (T-10M obr.1957):
Crew: 4
Lenght: 9,87m
Width: 3,56
Height: 2,43
Weight: 52t
Armament: 1x 122mm M-62-T2 & 2x 14,5mm KPVT HMG
Conclusion:
I personally think that regardless of what version would be chosen by the developers, if this tank is ever added, it would be a great vehicle for the German tech-tree, being a tank with decent armour, decent mobility and decent firepower, which for a heavy tank, is something Germany does not have many of.
Overall though, it seems most realistic and logical, that the T-10M would have been adopted, given the date of the order was 1957, and the completion was stated to happen around 1959, leading me to believe East Germany would have received the most modern version, the T-10M.
Any of the versions would be non-modified T-10’s with the exception of the NVA markings on the turret, which is why I think the markings on the Panzer X should probably be part of all camos and be unremovable, much like the unremovable NVA markings on the SPz BMP-1.
As for the name, I believe “T-10 / T-10A / T-10B / T-10M” would be completely adequate, although the name “Schwerer Panzer X / Panzer X” would be unique and cool to see, I think the standard “T-10” specification would spark less confusion.
How the markings could look (picture is an East-German T-54AMZ):
Thanks for reading and if you want to add or correct something, feel free to let me know.
Cheers! 
Sources
“Kampfpanzer der NVA” by Jörg Siegert and Helmut Hanske
“Soviet T-10 Heavy Tank and Variants” by James Kinnear and Stephen L. Sewell
