I didn't look for name meanings but all of them have amazing stories.
My first, my angel baby, was given the root meaning of my mum's name and Hope because at that point we didn't know where we would go from that about having more children. It turned out her names together were a promise from God that we would have another baby - my grandad preached on her name at her funeral.
My second was a name that just kept coming up in anything I liked or I'd comment on a character at the time with the same name and a horrible shortening and say mine wouldn't be called that. We gave her a middle name that was chosen during my previous pregnancy, after Mum and after the fact that I have always had a friend with this name (different friends!) Her name means gift of God (which blew us away after the first one) princess and carefree which describes her perfectly.
Second one we decided to give the middle names of his grandfather (or the feminine version for a girl) and his grandfather's mother. Because they are Welsh and both of us have quite strong family links with Wales we decided to look for a Welsh first name. Mum started listing all the Welsh people we knew from my grandparents church and any other names she could think of and our eldest latched onto a particular name, we decided we liked it so it stuck. The name she chose means gift of God! Her middle names are blessing and follower of God. Blessing is perfect for her, she's only 3 so can't comment on the follower of God part.
Third one was unexpected and we'd used up all the family names. Mum joked she wanted us to have another Welsh name but with lots of letters and an easy pronunciation. We chose two names that we really liked but they didn't go together so we decided to use his niece's name as they were really close (not now, we've found out she's done some horrible things to us) to link them. Her name means Love, Listen, Live which as Christians we thought was a nice motto to bring her up by.
No idea what we're going to do this time! We're really out of relatives especially as it's looking like another girl!