I depends on what you feel comfortable with being called.
The little kids in my grandsons neighborhood call me Nana -
like the boys do. My DDs friends called me Mama (first name) when they were at our house and their children call me Nana (first name). I personally feel that Mrs (last name) is too formal when you are around the kids all the time but, just being called by your first name is a little bit to informal.

I have the same situation. I have a step father and step mother. DH prefers them to be called by their first names. My step mother requested that my kids call her Noni. My grandmother was Noni but has passed away. DH has a little problem with this as well with his mother's husband wanting to be called Grampie.
They are not the kids blood relatives, so are truly not a grandparent. Maybe it is a little confusing for the kids, but I myself don't really have a preference. I too have Grandparents from my step dad, who has been with my mother for 32 years (I am 37) He has been more of a father than my bioligical dad.
What feels right for all of you? Have you asked your son and his GF?

how about Gin?

How about grandma D? Whatever you and your family feel comfortable with is ok.
Marie

This brings to mind a couple of traditional ways of handling relatives that are not really "kin" but part of the close family. I have aunt whose in-laws all called the older men and women in the extended family, sister or brother. It was Sister Mary, Brother Bill, etc regardless of relationship. Another way is used in my family. It would be Miss Mary, Mister Bill, etc. This is quite helpful when there are young children of cousins who need something to call the older cousins. I think that the step-grandparent could use either of these.

This gives the child a feeling of belonging by using the first name, but gives a title to show repect.

All adults close to us but without an easily defined relationship were "aunt" or "uncle." I did it that way with my kids and they do it with theirs. Personally, I'd have the kids call me Grandma. It's a title of respect and love more than a statement of biological relationship.

I would opt for Grandma or Nanna also. The kids are old enough to realize you are not their biological grandmother, but if they are fond of you, and you of them, it would give you all a family feeling towards each other. I also like Nanna (firstname) or Grandma (first name). The important thing here is to give a family feel to the relationship, and maybe the card was a bid for your approval of the common-law relationship and the feeling your son has for the kids.

My kids had a stepgrandmother named Virginia, and they called her Grandma Gin. The two names just fit together so well. She still was recognized as a Grandmother, but a little different from the two bio grandmothers.

it is very obvious that kinds love you like a Grandmother and they are letting you know by their card. Open your heart, it looks like after 7 years you have earned this cherished title. They love you and they would love if they can call you Grandma. Grandma+(your first name) would be nice. Can you send them card back signing it like that?? Your son, your DIL and they would love you for it even more.
Yes, children are old enough to know that you are not their blood relative, but they also know that they love you as Grandma. Please do not dissapoint them.

In the previous paragraph, I say "DIL". I don't know why they are not getting married (some people are happy just the way they are), but after 7 years living with your son, she should be looked at as DIL.
All the best to you and to your family.

When my stepsons had children, I was asked what the kids should call me. Since at the time there were two blood Grandma's also I decided on Nana. Now I'm the only grandmother the kids have and the only one the younger ones remember. I think the kids need the reassurance they are accepted, especially because there is no marriage. They need stability and this is an excellent start. The kids can't help it if the adults don't marry.

Let them call you grandma. I have two grandsons ages 17 and 18 who are not related in any way. Their mother decided to call me mom 20 years ago. (Her mother was no longer with us) I am the grandma from their mothers side.
I also have a cousin who is 15. Her grandparents on both sides live in other states and are glad she has me here.
All of them know I am not the grandparent by blood but they all love me as if I am. You can never give or get to much love!!!!
By the way, My son and DIL presented me with twin granddaughters 5 and a half years ago. I worried that the older ones would feel that they were not as important to me
But they love the little ones too.
Just love them.