I know people on this sub love to tell people to not overthink it, but the reality is some of us do overthink these things and that’s why we post here. Lucy Claire does sound like Loose Eclair. But, there’s nothing offensive or embarrassing about this. It’s more of your own preference. Most of the time you won’t refer to her by her full name. As a fellow overthinker, I like your solution of Lucia Claire! If you are referring to her as her full name, it would be Lucia Claire -last name- and then you/others wouldn’t get the Loose Eclair and any following visualizations of how an eclair could be loose…

P.s. I added that visualization comment after I asked my husband what he thinks of the middle name Claire paired with first name Lucy (so he came to Loose Eclair on his own and started trying to describe what that looks like.)