How are royal houses founded and named?

by SNRNXS

I tried researching this but it seemed a bit confusing the further I got into it. After about an hour and a half browsing Wikipedia I have come up with 5 main questions:

Is a house just another term for “family?”
Can anyone decide to create a house? (Of course it doesn’t become royal until it gains power)
Does a house need to control territory or have authority as a family to be considered a house? (Or can you have one even with no authority?)
When a house is founded can it be named whatever the founder(s) want(s)?
Also when a house is founded, does it only include those such as children and siblings of the founder(s), and not previous generations like parents? How distant did you have to be of a relative to be not considered a part of the house?

These are just some things I’m curious about. To me it seems like anyone could just say, “Today I’m going to create the House of _______,” and then create their own escutcheon and coat of arms (at least in the US where there is no heraldic authority). Of course that house would have no recognition nor authority unless a member of it became ruler of America or some sort of territory.

One question after another. As everything related to european middle ages and feudalism in general, you have to deal with a lot of stuff, which derives itself from tradition. Most of the the time there are no set rules, which govern what is what.

The term "House" is not a exact synonym of "Family", but is used very often as one. "Family in the most strict of definitions, is you, your spouse, your kids, and maybe your parents. In the most lose of definition it can be used as a synonym for "House", but it depends on the context of the situation. Saying: Me and my family are going on a vacation." does not mean your ancestors and familyline, obviously. Saying: "The Habsburg family ruled Austria for most of the middle ages.", does refer to the House of Habsburg.
A house, in the sence you are talking about, is not created by an individual. An individual may have anbitions to create a house from his family-line, and can lay foundations for it, but he/she does not have the means to create one directly. Houses in general are not created, but "grow" from succsessive generations of individuals in power, all hailing from the same ancestor, roughly said. If a house is created in the sence you asking, depends on general perception by the public, multigenerational prominence in a region, and finally at least one historian( or just social convention), saying: "Yup, this family was around for some time (generations) and held great influence on our cummunity. They hail from one ancestor, so lets call them a house."
Yes, a influence (power) is required for a "House". Of course, you can go and say that you hail from your grandfather, so you are the member of house "Grandpa", but it will (likely) not get accepted by your surrounding, nor historians in the future. (If you, your grandfather, nor your dad held no real power/influence). But be aware, that a "House" can be noble, but does not need to be. Examples of "Houses", which are not noble, are the great "finantial" dynasties, like the german Fuggers, or the italian Medicis. (But the latter ascended into noblehood, so it is intertwined). Generally power can come from military/landholding but can come from trade/finantial.
A house is not officialy founded (see above), they are aknowledged. What you have on mind are names of noble "houses". Which mostly hail from geografical origins of that "house". Habsburg is a castle in today Switzerland and the ancestral home of the Habsburgs. Simillary with the Hohenzollern (Prussia/ German Empire). Finantial Houses (Fugger) use the surname of the family.
Membership in a house is very fluid, from a historical perspective. Rule of thumb is a shared ancestor, and legit marriages. (No "bastards", marriage in adequate social class). There can also be sidelines, formed from events like succesions, relocation, or conflicts over heritage in the family.