It’s not required that you mention names, but it’s okay to mention names, and many of us like to do it especially if we’re thinking of someone specific.
However, if one prays a lot for others, pretty soon the number of names on the prayer list is way beyond the physical capacity of the person praying to reel them all off. Not to mention that we also want to pray for the forgotten and unknown strangers most in need of help, whose names no one knows or remembers.
I currently have dozens of living and deceased people on my prayer lists. When I pray I will likely mention one or two who are most on my mind but that’s about it because I cannot sit there all day reciting 50 or 100 or 1000 names. Like last night I prayed especially for Pope Benedict who is ill, a friend of mine who has COVID, and a recently deceased TV personality who I liked to watch. And everybody else goes into the general bin of “all the poor souls in purgatory” or “everybody on my prayer lists and everybody most in need of help.”
So, your husband is correct, you are not required to mention the names every time you pray. If you like to mention names, and you can do so without it being very burdensome on yourself, then feel free to choose to do so, but you don’t have to.