hi marylen!
i will share to you what i did based on my experience. when i get my NBI Clearance, I did use my married name, it was ok, no problem with it, thats what i also submitted to UKVACS.
I also updated my savings account at BDO, its not necessary tho.
But i think you need to update one valid ID with your married name in case you're going to use the latter for your flight tickets to manila. The vaild ID is what you're going to show upon check-in at airport, considering that your passport will be submitted to UKVACS.
hope this helps!