Looking on the internet deeply has found these results:

beingaloof is the most popular phrase on the web.

staying aloof 121,100 results on the web	beingaloof 1121,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
He's just been so aloof lately, always staying late at work, never has time for my calls.	It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

staying aloof

121,100 results on the web

beingaloof

1121,000 results on the web

More popular!

He's just been so aloof lately, always staying late at work, never has time for my calls.

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.