The Lubavitcher Rebbe would often learn out something from the name of the Parsha. In this Sicha from Parshat Toldot, 1992 (quoted in Alex's answer to your other question), the Rebbe reiterates some of his guidelines about the Parsha name. (See the footnotes there for other places where the Rebbe discusses this)
The name that was chosen is usually at the beginning of the Torah Portion (either the first word or the first unique word). But Jewish custom has established the name, and "Minhag Yisroel Torah Hee". A Jewish Custom attains the level of Torah, and like Torah, it is incredibly exact.
There are Parshot where the first "eligible" word is not chosen (e.g. Noach and Toldot), which proves that the names given were not just the first convenient word.
A name in Lashon HaKodesh is not just a label, but also is an insight into the essential nature of the thing. (cf. Adam naming the animals). So too, the name of the Parsha is an insight into the Essence of the Parsha.
- In footnote 10, the Rebbe points out the Shelah, who says that reading the names of the Parshot is considered as if one learned all the Parshot in depth.
If the accepted name of a Parsha has changed (e.g. Parshat Metzorah used to be called "Zot Tehiye" - see Likutei Sichot vol 7, page 103), this teaches us something as well.
There are probably other rules I can't think of right now.
Based on these rules, the Rebbe would often point out how the connection between the name of the Parsha and the content of the Parsha, and what we could learn from the name.
There are two sources (that I can think of right now) that collect all the Rebbe's lessons from the names of the Parshot.