Do you get asked for birth certificate in the border (when entering the UK/other countries)?

My husband's last name is an Eastern European name ends with -ki (and for female it will be -ka). I didn't change my surname when we got married. We're now pregnant with a girl who will take his surname, but the female version.

I heard that in the border they might ask you for a birth certificate if you have a different surname.

Wondering if you know: 1. Will they ask you for a birth cert if it's the same base surname but with the male vs female version? 2. Will adding my last name as the kid's second middle name (not hyphenated last name as it will be excruciatingly long) help at all, or is bringing birth cert inevitable anyway? 3. For those with the exact same surname, have you ever gotten asked for birth cert?

I know it's not that big of a deal to bring a copy of birth cert but thought I'd explore the options to avoid potential future hassles.