See the results of this poll: Thiago pronunciation
Respondents: 35 (This poll is closed)
- tee-AH-go : 34 (97%)
- chee-AH-go: 1 (3%)
I’d pronounce it tee-[name_m]AH[/name_m]-go as well. I am aware the correct Portuguese pronunciation is chee-[name_m]AH[/name_m]-go but I don’t think this would ever be correctly said outside of Portuguese speaking countries.
I’m from a Portuguese speaking family and speak middling Spanish as well, so I will wade in.
Essentially both are right, as the previous poster said. The pronunciation you are familiar with is the general pronunciation in Spanish, and I would say the most common pronunciation in the U.S. and probably much of Europe where people are relatively familiar with the very basics of Spanish.
In Portuguese-speaking countries and among people that have more contact with Portuguese most people (it does depend on your accent) pronounce [name_m]Thiago[/name_m] (or [name_m]Tiago[/name_m], they’re pronounced the same) chee-[name_m]AH[/name_m]-goo. I added two Os, because the ending does not sound the same in Spanish and Portuguese. In Portuguese [name_m]Thiago[/name_m] is pronounced with a long O sound like moose or goose or loose, and in Spanish it is pronounced with a short O sound like in hose or toes or woes.
So, Spanish = tee-[name_m]AH[/name_m]-go
Portuguese = chee-[name_m]AH[/name_m]-goo (long O)
All this being said, in the U.S. overall I think most people would use the Spanish pronunciation. You say you are in [name_m]New[/name_m] [name_u]Jersey[/name_u], and there are a good number of Brazilians in that area of the east coast so you might get the Portuguese pronunciation sometimes as well. I guess it comes down to if you care. Personally, I like the name [name_m]Tiago[/name_m] and would consider using it, and am comfortable with the fact that my partner’s Spanish-speaking family and the wider community would generally use that pronunciation, and that my family (particularly my mom…) would probably not be able to NOT use the Portuguese pronunciation. I would probably use the Spanish pronunciation when speaking English or Spanish, and only use the Portuguese pronunciation if I was speaking Portuguese.
I agree 100% with @beort12. I am somewhat familiar with Portuguese and Brazilian names so I was aware of the correct pronunciation (chee-[name_m]AH[/name_m]-goo in Brazilian Portuguese). However, English speakers would never think to pronounce it that way.
My first thought was thee-[name_m]AH[/name_m]-go. Kind of like [name_m]Diego[/name_m] with a “TH” instead.
I voted for tee-[name_m]AH[/name_m]-go, but I just noticed I pronounce it like chee-[name_m]AH[/name_m]-go. 
I am Brazilian btw. Like [name_f]Eryn[/name_f] said both ways are correct, there are variations within the Brazilian Portuguese language too. [name_m]Just[/name_m] go with your favorite prn., but be aware that people who speak Portuguese or Spanish may say it differently and not notice it (aka they may not hear a difference, so they will continue to pronounce [name_m]Thiago[/name_m] their own way).
In Portugal’s portuguese we would say Tee-ah-goo like [name_m]Santiago[/name_m] minus the San. Brazilians say it the chee way. In english, I would pronounce pretty much like in portuguese.