And it doesn't matter if it's a Russian name or not, as long as it can follow the rule, which is that it end in a consonant. Zhao is a problem.
Donald John Trump son of Frederick
Дональд Фредерикович Трамп
Donal'd Frederikovich Trаmp
Stresses: DO-nal'd Fre-de-RI-ko-vich
In conversational speech it's free-dee-RI-kich. That -ovich long ago was reduced to -ych or -ich. Very stiff pronunciation of the patronymic is free-dee-RI-kuh-vich, lots of brief syllables with the dee-RI middle being longish.
Stress doesn't change from the root name used in patronymics. In surnames, though, if there's an -ovich of Russian (or East Slavic) origin then it's stressed -O-vich. Voinovich has stress on the middle syllable. Yanukovich is stressed on the "o". (If they're Serbian or Croatian in origin, stress pulls back one: Milosevich isn't stressed on the -ovich, but the preceding syllable. The e/o change is normal, but don't ask.)
The ' in Donal'd is because Donald is there because l and l' are different sounds, and Russians pronounce "Donal'd" with a palatalized l'.
It's "Tramp" and not "Trump" with a "u" because in English it's more like "truhmp." That uh sound is much closer to a Russian "a" (sort of like in "father" but not as long in duration) than to a Russian "u" (like the oo in "boob"
.
No, it's nothing like the English word "tramp", which in Russian would be written "tremp" because the "ae" sound in words like "tramp, fan, can" is much more like the Russian stressed "e".
Frederick isn't a Russian name, but it's been around long enough. Google the patronymic and you get a fair number of hits. Many are immigrants, some are historical (when German influence in Russian was much higher than today). After WWII it would have been avoided.
One important point: Even the Wiki page (always a valuable place to check for oddball vocab) avoids his patronymic. It has "Donal'd Dzhon Tramp" because he's not a Russian speaker and the only time you'd use the patronymic is if you're in Russian or carrying over how you usually refer to somebody in Russian. So you can form the name, but he's not integrated enough for it to matter.
Very few Russians have bothered to use my patronymic (Robertych), and most did so because they were uncomfortable with US norms and felt a psychological need to have something in that linguistic space. Otherwise we've either kept my first + last name (formal), full first name (seldom done in Russian), or used a hypocoristic. Hypocoristics are shortened names: Theodore may be Fyodor, but there's Fedya, Fed'ka, Fedochka, two variants of Fedushka, etc. In English we only have Ted and Teddy, and bizarre things like "Teddykins". Perhaps Igel would become Izha.