I am looking for an answer referring to the logistics lore-wise and in terms of mechanics in general.
According to the Sword Coast Adventurer's Guide (page 20):
The Faerunian pantheon isn't the only one known on Toril. ... people in faraway lands are known to worship altogether different gods. Occasionally, foreigners bring the worship of these gods to Faerun. In addition, on rare occasions a new god comes into being, ... In cosmopolitan places such as Waterdeep and Calimshan, small shrines and temples to strange gods spring up from time to time.
Over generations, a new god might become a settled-in member of the pantheon. Indeed, some scholars posit that Faerun has many "immigrant" gods, who joined the pantheon's ranks so long ago that their foreign origins are lost in antiquity.
Some examples of immigrant deities include Tyr, Mielikki, Oghma and Loviatar. Such "interloper" or "multi-spheric" deities have been a part of the Forgotten Realms setting from its very inception by Ed Greenwood (see Dragon magazine issue 54 from October 1981). So it would not be unusual to put in a cleric of Thor if your DM does not object to it.
(It is worth noting that in the older editions of the game, if you were a priest in a crystal sphere where your deity did not have an established base, you would not be able to receive spells above the 2nd level. You would have to use a special spell called Contact Home Power to (partially) overcome this limitation. However there is no such written constraint in 5e.)