"the" is in my business name, capitalize it or not?
The name of the business would be a proper noun. Wikipedia gives an example of a multiple word proper noun in which the word "the" occurring as a middle word is not capitalized:
http://en.wikipedia.org/wiki/Capitalization
"In nearly all European languages, single-word proper nouns, including personal names, are capitalized (like France or Moses). Multiple-word proper nouns usually follow the traditional English rules for publication titles (like in Robert the Bruce)."
"These are the words that should be capitalized in titles:
- The first and last words of the title
- All nouns, pronouns, verbs, adverbs, and adjectives
- Any conjunction or preposition of five letters or more --(This is optional. You can choose to go with an older rule that says not to capitalize prepositions or conjunctions regardless of length. The five letters or more standard has developed over the last two decades or so. Either form would be acceptable, as long as you use it consistently.)
These are the words that should not be capitalized in titles:
- Articles (the, a, an), unless the article is the first or (less likely, of course) last word of the title
- Prepositions of four letters or fewer (unless the preposition is the first or last word of the title)
- Conjunctions of four letters or fewer (unless the conjunction is the first or last word of the title)
- The particle "to" used with an infinitive (unless the "to" is the first or last word of the title)"
Your case falls under the first bullet of what not to capitalize. So, in this case, do not capitalize 'the'.
http://grammartips.homestead.com/caps.html