SELCAN HATUN!!! Anyone watch Ertugrul :D literally the only reason I'm learning Turkish XD. Reply if you know what i mean, I need Ottoman Empire friends (hehe).
Ben is literally "I" so when I say Ben Tom, this literally translates to "I Tom". Sen is literally you so "Sen Julie" literally translates to "You Julie". I like to think of it from the context of Turkish being an original language. The translations have been modernized of course but...
I've found that a few (non-Romance/Germanic) languages drop the "to be" for short declarative sentences. The logic is that, if you're listing two nouns, or a noun and an adjective, you're obviously equating them, so why bother throwing a verb you'd have to conjugate in there? It even kind-of works for us; it's not proper English, but any English speaker would still understand "Me Tarzan. You Jane. Food good. Fire bad." perfectly fine.
Same in Russian. To use "to be" explicitly it could be archaic, with an added emphasis (Я есмь (archaic form of есть) царь! = I am the king!). The m-dash can be used in similar function (Я — царь).
Also, "to be" can be used to jokingly demonstrate the foreigners speaking broken Russian as they try direct translations of their languages (western Europeans).
Reminds a little of the old tarzan movie. I tarzan you jane. Not to make fun of it btw. This really helped me to get the logic behind that actually simple sentence structure. But i just started with the course and the structure is totalky different to all other languages i speak/know.
I like to think of it as :
B-: First person
S-: Second person
Biz? First person + plural, so "we." Sen? Second person ＋ singular, so "you/thou"/ (as opposed to "you all/y'all/yous"). I know that doesn't account for 'plural you as polite you', but that seems to be pretty common in most non-English languages, so you could assume that and be correct here.