At my most recent job there was already a Chasity so I chose to go by middle name, Rose. As a child I always wanted to use it. I liked it, but I have long since made my peace with my name and really like it now so I did miss hearing it.
Also, I dislike my nickname. Family and close friends call me Chas, with an S- I will shoot eye daggers at you if you pronounce it with a Z. It's ok. And the girl at work was Chas. And I've had other jobs where they shorten it to Chas. But I don't feel like a Chas. I feel like a Chasity. In fact, I knew that I wanted to marry my husband one of the first times he said my name. I knew I could hear him call my name the rest of my life. Except now I usually only get Honey, lol!
All that to say, I like names that have several actual nickname options and not just shortened forms. I had to go by Rose because by the time you'd say Chasity, the Chas would have come running. So Theodore could be Theo, Ted, Teddy. You already gave examples of Margaret, our leading girl name. Leading boy name is William, most likely nn Will but maybe Billy, Bill as an adult, there's Liam also.
And even with a name as uncommon as my own, you might still end up with more than one in your circle and it might be nice to have more options than just one nickname or a full name.