Should terms like "Googliness" be capitalized?

Should terms like “Googliness” be capitalized?

It's not obligatory.

It's a fun neologism not to be taken seriously, googlism is not and will never be a proper noun. The proper noun is Google, and it should be capitalized at all times.

Its verb form “to google" and its inflections googles, googled, googling, can be left lowercase, but this is very much a subjective thing, and I have seen it capitalized in instances such as “I Googled your name" and “If I Googled XYZ” but it is nearly always lowercase when it is a gerund. For example, “Will googling XYZ get me into trouble?”

AP style is to capitalize “Google” when you use it as a verb, when you say you Googled something or are Googling something. The Chicago Manual of Style also says to capitalize trademarks such as Google, but notes that although this is what corporations would prefer, it’s not a legally binding rule, and they note that Webster’s includes lowercase entries for both “google” and another company name that has become a verb: “xerox.”

The Merriam-Webster Online Dictionary lists the verb "google" as lowercase, but notes that it is often capitalized. The Oxford English Dictionary entry shows the verb "Google" capitalized, but says it can also be lowercase. Garner’s Modern English Usage says it can go either way but that it’s more common to keep “Google” capitalized than to write it lowercase.

The bottom line is that you don’t have to capitalize it unless you're following AP or Chicago style, but it’s probably a good idea to do it anyway. No matter what you decide, pick one way of doing it and being consistent instead of flipping back and forth between two styles. Be deliberate.

Quick and Dirty Tips

It looks like this word was invented by Google themselves, and speak about what they think it means in this blog post. They mention it three times, including the page title, and all of times are capitalised:

The simplest answer may be the right one: Googlers themselves. Other companies screen for intelligence and experience in potential recruits. But Google also looks for “Googliness” – a mashup of passion and drive that’s hard to define but easy to spot.

Google looks for "Googliness”: a mashup of passion and drive that’s hard to define but easy to spot.

I would consider this word fairly corporate and not as integrated into the language as the 'sandwich' example given by @WeatherVane above, so would capitalise.

Google is known for pedantically capitalising and protecting the intellectual property of the word 'Google'.