're: mudra's case
The right venue to change your son's surname, and not using the surname of his original father, is via Adoption. If you do the late registration, that's committing a falsity in a public document, hence, you might be liable for falsification of public documents --- that's one complication that you don't want to face.
Besides, adoption done legally, protects the rights of your kid, because she/he becomes legitimate. The late registration, if proven incorrect, nullifies the document, hence making him/her illegitimate, and as stated, endangers you for a possible prosecution.
re: ms. gemini; beneficiary
Is your child, the only child of his father? If so, the child can be the sole beneficiary to the exclusion of others --- that is kung unmarried din sya. Kung married and has other kids, she/he can still be a beneficiary, subject to the percentage contained in the succession.