My dad (Donald) has the Hebrew name of David. Since that’s my English name, they chose Yisrael for my Hebrew name - I’m not named after any relative. I’m the third child and they just went with names they liked.
To return to the OP, I’d guess that your brother’s Hebrew name is probably Mordechai, as others have already noted.
Interesting stuff about why American Jews have “Hebrew” names that don’t reflect Legal names that are perfectly good Hebrew names as well… Learn something every day 
And as you happen to know, our grandfather’s name actually WAS Mordechai, making that even more probable.
Right. And on the assumption that (I’m inferring, based on our previous conversation) your brother was born after your grandfather’s death nearly cinches it.
If your brother is the eldest son, and especially if he is the eldest grandson, I’ll make it 99.9% certainty. 
I wonder if this custom actually originated the other way around. An immigrant from eastern Europe with a Jewish name comes to America, and picks out a nice safe American name to use in public. When his kids are born, he gives them Jewish names, but puts some nice safe American names on the birth certificate. So these kids have an “official” American name, but a private Jewish name. And then when their kids are born, they give the kids an American name, but think, “Oh yeah, better give them a Jewish name too…”.
Could be. Though where my mom grew up, in Poland, she had her everyday name in Yiddish and her Hebrew name in shul. She picked a related English name here in the States. I think she used her Hebrew name when she lived in Israel.
My brother was born in Israel with the name Mordechi and in England he goes by Marc - which is also the name on his English passport. It’d be hilarious to be able to tell him that he should be called Michael.
Fiendish Astronaut:
There’s really no “should” there. When Jewish parents want to assign an English name to their child, they can choose anything they want, even a name that’s totally dissimilar. I have a friend whose Hebrew name is “Chanan” but has an English name “David”. (And no, “David” is not his middle name in Hebrew.) It’s all about giving the child a name you feel he (or she) won’t be embarrassed to use in public life. In a society where foreign-sounding names might be a stigma, you pick whatever name you think sounds most “native.”
Of course, this attitude made more sense in prior generations. Nowadays, strange ethnic names are so common (in America), that Jewish ones are hardly worth worrying about.
No one said should- just what’s typical. Just like you might have someone whose nickname is Jack, it’s typical their full name is John. But you might meet someone whose full name is Jackson using that nickname.
I’m lobbying for Shoshanna for my kidlet, as it’s a perfectly good name in English and Hebrew and my other great-grandma, the one I knew, was called Rose.
However, even in her ketubah, she is called ‘Reitzel’ (the Yiddish equivalent). As far as we know, she either never got a straight up Hebrew name or never knew it. My own name is Yiddish, rather than Hebrew, too.
Is it possible that your brother doesn’t have a standard Hebrew name and was actually just called ‘Mottel’?
I love Shoshanna! Great choice.
‘Hebrew’ names can be Yiddish. It’s possible his Hebrew name is Mottel. One of Lil’ Neville’s Hebrew names is Zelda, which is Yiddish, not Hebrew. Mr. Neville’s mom’s family came from Latvia, and had a tradition of Yiddish names.
MickNickMaggies:
While it’s true that many Jews have only Yiddish names as their “Hebrew” names, that’s generally when the name is a Yiddish word, not a Yiddish-ized version of a Hebrew name. I’ve never heard of a “Mottel” as anything but a diminutive of Mordechai. Though of course anything’s possible.
My niece’s Hebrew name is Simma, after our wonderful Bubby. Bubby’s English name was Sylvia. My sister did not like the name Sylvia. She gave serious consideration to just using Simma for both her daughter’s names. In the end she went with Skyler and Simma as a Hebrew name.