Some have stated that there are three aspects of Jewishness:
1. Ethnicity (Hebrew)
2. Religion (Judaism) (includes culture)
3. Nationhood (the people of Israel)
While it is possible to guess that some individuals are Jewish, based on their physical appearance, clothing or manner of speaking, I have met many, many Jewish people who don't "look Jewish," so it is impossible to generalize, just as it is impossible to generalize for people from many other backgrounds.
I have a mixed heritage: English, Irish, Scottish, French and Jewish. People can usually guess the Scottish and Irish part based on my hair colour and complexion. People can't guess my husband's ancestry, even though he is also part Irish and Scottish.
I worked for several years for a Jewish organization. The Jewish people whom I met usually knew right away I didn't fit into #1 but, given where I worked, assumed I had either married a Jewish man and/or had converted to #2. However, the non-Jewish people whom I met assumed that I was #1 and #2.
I met the Prime Minister of Canada at a work-related event during Channukah. Since he knew my employer, when it was my turn for the handshake and photo opp, the PM wished me a Happy Channukah. The funny part is that I automatically responded, "Thanks, you, too!" Two Christians wishing each other Happy Channukah -- too cute! And so typically Canadian in its politeness.

Anyway, my Jewish ancestor had a typically English name, so that was no clue whatsoever to his religion and heritage. I only discovered it when I couldn't find records for him and his wife and children in the local parish registers. Well, it took more than that, because at first I thought maybe he was Catholic. It actually took a few years and the assistance of others to find the records that proved it. I'm still trying to find out who his parents were (I have to have the $$$ to hire a researcher who can read Hebrew).
Oh, and I'll add that my Scottish ancestors had big noses, and I've had Jewish friends with noses smaller than mine.
Good luck and have fun with your searching!
Josephine