You text him every morning around 6 am? I honestly think that might be a little much but that's just my personal opinion. I'm 22 and I don't even text my friends or boyfriends that often (when I am in a relationship).
I'm not sure how old you two are, but if he's older than 30, texting every single day just might not be his cup of tea.
I can easily go 2 or 3 days without texting someone even if I'm in a relationship with them...so he just might not think it's a big deal.
If you bring this up to him there is a chance it might push him away because it does sound a little clingy. You've been dating a few months, but are you in a serious relationship or is it just casual dating?
Anyway...yeah I think texting every day is excessive, so if I were you I'd really pull back on that, especially since you both work every day and sound like you have busy lives.
You can always call him after work and just talk about your day instead. But I dunno about every day.