Am considering Second Generation or Second Childhood as mane for children's consignment store. What do you think? Any other suggestions?

Neither of those names is available as a .com domain name so I would advise against using either of these names. Since you're just starting out, there is no reason for you not to name your store the same (or as close to) your domain name. You may not want a website right away, but you should at least get the name for the future.

I would also recommend that you not limit yourself to just children's consignment. When mom comes in to bring in kids stuff, she may want to find stuff for herself

Every time I think of consignment, I think of stores like Plato's Closet. The name is simple and easy to spell. Do you have one word that you like specifically?

your word consignement
your word store
your word closet
your word resale
your word clothing

Good luck!

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Thanks I'll keep that in mind, good advice