You are trying to be knowable enough to be trusted and careful enough to be safe. Those pull in opposite directions, and the resolution is sequence: share more as trust is earned, rather than deciding once at the start.
Start with what cannot be searched
What you want, why, what you will not compromise on, roughly where you live. This is the substance people actually need in order to know whether to talk to you, and none of it identifies you.
Hold back the identifiers
Surname, employer, the name of your street, your children’s school. Individually harmless; together they are a complete profile. Assume anything you share can be combined with anything else you have shared.
Photographs
A photo used elsewhere online can be reverse-searched to the account it came from. If you want your profile photo not to lead back to your other life, it needs to be one you have never posted anywhere else.
When to open up
After a first meeting, not before it. Before anything is agreed, not after. There is a window where you know enough about someone to share your surname and still have the option to stop — that is the right moment, and it is later than most people think.
The reciprocity test
Watch whether disclosure is mutual. Someone who accumulates detail about you while offering little back is not being private. They are being asymmetric, and that asymmetry is the thing to notice.