As far as I know
Claire used to be very popular in Britain (top 5) for a long time.
Clare was quite common too. Maybe a British person would know if it feels bland and banal now. To me it sounds nice and pretty, but I much prefer
Clare over
Claire and
Clara over both of them.
Yes, as a middle name it feels really bland and standard. But I do think it sounds nice and I like the meanings ("lake" in English and the Chinese
Lin means "forest" or "jade"). It has a very green, white, yellow and blue nature-image to me personally. Just like
May.