Kelly Osbourne says one of the biggest fights she had with her baby daddy all had to do with their kid's surname ... and it sounds like it's a fight she eventually backed down from.

Ozzy and Sharon Osbourne's famous daughter opened up about the huge argument with her man, Sid Wilson, on "The Osbournes Podcast" ... telling her parents her partner didn't want their son Sidney to have both their last names when he was born in 2022.

Kelly says she and Sid -- who she's been with since early 2022 -- couldn't see eye to eye about giving their son two last names, and ultimately it appears Kelly capitulated ... 'cause she says Sidney isn't an Osbourne in name.

Osbourne said she and Sid are moving on ... but that she also may never truly be able to forgive Wilson for seemingly forcing this decision upon her. So yeah, harsh feelings linger.

There is light at the end of the name tunnel though ... Osbourne said she and Wilson have been talking a lot -- and attending couples therapy -- and she says he's seeing her side of things.

Kelly added that the couple plans on changing their son's name to include both of their last names ... a smart move according to her parents who pointed out how beneficial the Osbourne name will be for the kid's future.

After all ... lots of people in Hollywood use their famous family connections to book jobs -- including Kelly, who recently said she was proud to wear the "nepo baby" moniker.

Kelly told Rolling Stone back in January she was proud of her parents' accomplishments, and she had no issue being associated with them -- though she added she doesn't think opportunities should fall in her lap because of her family ties.