In the late Third Age, Dúnedain usually give their children Sindarin names. Also, we often recognise a Dúnadan's name not just as an elvish name, but as the name of another known elf (Ecthelion, Denethor, Mablung, etc.)
The princes of Dol Amroth seem sometimes to cling to the native Númenórean language Adûnaic, but elsewhere that is avoided among Elf-friends since the end of the Second Age because Adûnaic is usually associated with Black Númenóreans. Given the history with Angmar, we can expect this in Arnor all the more.
We may expect some Westron names, especially for Gondorians/Arnorians who are not descended from Númenóreans, but if that's the case, then at least I don't know of any such example.
In the Second and early Third Age, royal Dúnedain were named in Quenya, but, at least for royalty in Arnor, those times are gone for more than 2000 years, and also stewards of Gondor choose rather Sindarin names.
Regarding commoners, we have fewer examples, but we already find traces of Sindarin in Dúnedain-names more than 5000 years before Lotr (Núneth), and lots of them during Lotr (Mablung, Beregond, Halbarad, etc.), so Sindarin is the language of choice for an Arnorian/Gondorian, especially if they are descended from the Elf-friends of the Second Age.
Since every Sindarin name has a meaning, I'd say you can choose any Sindarin name you want, as long as the meaning makes sense in the context. Just avoid names starting with Ar- (Aragorn, Arathorn, Arveleg, Argeleb, Arvedui, etc.). That's for royalty only. For the heirs of Isildur that's fine, for everyone else not so much.
Also mind that in the Dúnedain dialect of the late Third Age, y is pronounced like i, whereas ch is h in the middle of a word, and it's -k at its end. So Classical Sindarin Rocheryn (horse of the lady) would be in Arnorian Sindarin written like Roheryn, and probably pronounced Roherin.
Here are some names that are Sindarin and borne by Dúnedain. Sometimes Tolkien didn't translate them, but most of the time we can guess their components.
Alphros (maybe swan-foam),
Baranor (maybe hot fire),
Belecthor (maybe mighty eagle),
Beren (the bold),
Bergil (maybe valiant star),
Boromir (steadfast jewel),
Borondir (steadfast man),
Damrod (maybe hammerer of copper),
Denethor (maybe lithe-and-lank),
Derufin (maybe manly hair/intelligence),
Duinhir (lord of the river),
Egalmoth (sharp uprising flower),
Elphir (maybe swan-lord),
Eradan (single man),
Faramir (maybe jewel of hunt(ing)),
Findegil (maybe skilled pencil),
Galador (maybe lord of light/tree),
Herion (maybe son of the lord),
Hirgon (commander of the lord),
Húrin (vigorous heart),
Iorlas (maybe old leaf),
Mablung (Heavy Hand),
Saelon (wise man),
Targon (maybe noble lord),
Udalraph (the stirrupless (rider)),
Fíriel (mortal maiden),
Galadwen (tree maiden),
Ioreth (old woman),
Ivriniel (daughter of ivrin),
Lothíriel (maybe daughter of the flower-lord),
Rían (queen or crown-gift),
Beleg (the great/mighty),
Celebrindor (silver lord),
Dírhael (wise man),
Halbarad (maybe high-tower),
Malbeth (golden word),
Mallor (maybe the golden),
Malvegil (golden sword),
Thorongil (eagle of the star),
Gilraen (one adorned with a tressure set with small gems in its network),
Núneth (woman of the west)
Many of them appear in Lotr, so if you don't want anyone to get confused by associating the name with someone else, don't use these:
Anborn, Angbor, Baranor, Beregond, Beren, Bergil, Boromir, Damrod, Denethor, Derufin, Dervorin, Duilin, Duinhir, Ecthelion, Faramir, Halbarad, Hirgon, Húrin, Mablung, Targon, Ioreth.
Also, the names Baranor, Dírhael, Herion and Ioreth - though well known from Tolkien - appear in Shadow of Mordor as well, and, whether you accept that as canon or not, you might want avoid them too.
I hope this helped.