Hello! Would appreciate any thoughts/perspective on using William as the formal given name and calling our little guy Liam or just naming his Liam outright. I've been thinking about this way too much and I'm really on the fence!

Siblings are Stella and Elise. Our last name is three syllables and challenging to pronounce (has an "L" in first syllable, an "S" and long "I" sound in the middle, and ends with "TIS"). Middle name is two syllables, starting with a "Y" sound and ending in "AS". I like the options as he grows with William, but do not prefer some of the traditional nicknames associated with it. I also like that Liam is short and goes along with the shortness of our entire family's names (husbands is 4 letters and one syllable, mine is 4 letters and two syllables). The popularity of both names doesn't bother us (William is actually more popular in our part of the country than Liam), since we have such a unique last name and the total number of babies getting the popular names is much lower than when we were growing up.
Thank you in advance!
Re: William with nickname Liam or just Liam?
If we have a boy he will be William, so I may be a little biased
Baby #2 Due 3/7/20
FWIW, DS is James. Not Jim/Jimmy/etc.; just James. We always introduce him as James and that's what people call him, so I would expect that if you always introduced him as Liam it wouldn't be an issue.
TTC since September 2012
But please don't be like my SIL who lied for two years and told us all her son was legally named Liam, and then admitted it was William.
My brother and I both have nicknames like this from birth, and it's a pain in the butt. We have both named our children names that don't have nicknames/what we will call our children.
Marriage: 4/2008
Baby Carriage #1: 5/2012
Baby Carriage #2: 1/2016