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In the questor imperialis section of the index it says
Throughout this section you will come across a keyword that is within angular brackets <household> this is shorthand for a keyword of your choosing.

<household>
With the exception of free blades, all imperial knights belong to a household - a noble house which owes it's allegiance to the imperium or the adeptus mechanicus...

In the designers commentry it says if you can choose a keyword such as <regiment> for astra militarum could I choose blood angels.
It says no and gives the reason that blood angels is not a regiment of the imperial guard

If my knight owes it's allegiance to mars can I pick Mars as it is a mechanicus world?

Whats the question?

Sorry my phone was being odd I had to submit then edit question is there now

Also I would add that next to the household rule is a picture of a mars colour mechanicus knight with Mars skitarii

I mean, you'll note that the FAQ isn't actually trying to lay out clear rules for what faction keywords you can use (because this is complicated) but is instead gesturing at what's intended and saying that you can't be picking your faction keyword to try to benefit from cross-list synergies. You could make your Knights' House "Mars" but this would be distinct from the forgeworld keyword "Mars". The FAQ really could not be clearer that trying to pick the same name for two different types of faction keywords is exactly what it does not want you doing.