Is it unmanly to take wife's last name in marriage?

Non unmanly, but uncommon.

Taking the first name is much worse. Felicity, Rebecca, Chantal, Charmaine, Mandy etc.

Not at all. Not sure why this is even a question. Nobody cares what name you took but you two. Pick whatever name you like the best. It's your marriage, not anyone else's.

I think it’s embarrassing when a man does that.

Just a bad idea.   Tradition.   And, it makes it harder to figure out who married who.   And, it makes it hard to find things out family trees, ect.     Wife can take a name with both last names is the best option.    Or both husband and wife take both last names.   But a man to drop his last name completely, bad idea.

Is it unwomanly to take the man's last name?

This is a very silly question. It shouldn't and doesn't matter what you decide to do about surnames. It has nothing to do with femininity or masculinity.

One solution I liked (friends of mine did it) was for each partner to keep his or her own surname and for one of the kids to get his and the other to get hers. 

However, I also know a couple who decided that he'd take her surname, because it was a lot easier to spell and pronounce than his.  He says it's a relief not to have to explain his surname any longer. "Manliness" didn't come into it.

It is unusual to take the wife's last name in marriage. It should be the other way around .Wife should take the husband's last name in marriage. You may face a problem in registering your marriage.Discuss the matter with Registrar of marriages. It is important to clarify the legal aspect since marriage is entering into a legal relationship.

depends on the person

not at all, or at least i dont think so

It's gentlemanly