Grammatically, it is correct. The golden rule in English is never to end a sentence with a preposition (formally), although (informally), particularly in speech, this frequently happens.
No. 1 here is more formal but you could possibly use no. 2 if your text is more informal in tone. Indeed, in this case, you're simply ending a clause with a proposition but because it's immediately followed by another clause (no context given in your example), it sounds (perhaps is?) acceptable.

1. The reseller, under whom the current user is logged on, ...
2. The reseller, who the current user is logged on under, ...
3. The reseller, under whose system the current user is logged on,...

Also, if reseller is a system, as opposed to a physical person, you would have to replace 'who'/'whom', with 'which'.

Vielen Dank, dann bleibe ich bei meinem Vorschlag. Reseller sind bei uns eine besondere Art von Benutzern, die dann eben auch selber Rechte im System haben.

Sure, but don't forget the punctuation (commas) in your version.