Sorry, i can't recall your previous post, but i assume your child is small(ish)?
If so, she is acting this way from insecurity. If you have recently split up from her dad, she will be feeling seriously insecure, and any visitors are seen as a threat to her stable home with you, and she is kicking off to try and prevent anyone taking you away. Easy enough - embarass you, make you look foolish, hope this man will not come back.
If it is early stages, why not see him outside the home for a while, and if it looks like it may last, introduce him very gently, on neutral ground, and take it very easy, telling your daughter that she has nothing to worry about, and she is first in your life, and you ar not going off without her.
As an adult, and a mum you take these things as read, but an insecure child doesn't, and needs reassurance, not to be excluded by you in temper.
Have a 'girly' day out, and have a neutral chat about friends, nothing heavy, and then do your dating in private for now, so your daughter gets the undivided attention she needs right now.
Of course you are entitled to a private life - so make it privae - easier all round for everyone.
Good luck.