Would Texans still consider themselves American?

That would be up to each Texan, and independence does not take the choice away. Identity is personal. A change in which government Texas answers to does not reach into anyone's heart and rewrite how they see themselves.

Identity is yours, not the government's to assign

How you identify is not issued by a capital. Plenty of people hold layered identities with no contradiction at all. Someone can be Texan, and feel a connection to the broader American story, and be a citizen of an independent Texas, all at once. Independence settles a question of government. It does not hand out or take away the labels people choose for themselves. Those stay with the individual, where they belong.

Texas has always carried a double identity, and it works

Texans have lived with a strong, distinct identity inside the union for generations. The Lone Star, the pledge to the Texas flag, "Texas, our Texas," a history taught to every Texas schoolchild. People have been proudly Texan and part of the larger country at the same time their whole lives. Independence does not break that habit of mind. If anything, it formalizes what Texans have always felt: that Texas is its own place.

Shared history does not disappear when the flag changes

Independence does not erase the past. The history, the family ties across state lines, the cultural threads that run through the continent, all of it remains. Britain leaving the European Union did not make British people stop being European in the cultural sense. A Texan who feels American in heritage and values will go right on feeling that way. What changes is the government, not the bloodline or the story.

Citizenship and identity are two different things

It helps to separate the legal question from the personal one. Citizenship is a legal status. Identity is how you feel and what you claim. They are not the same. An independent Texas would sort out citizenship through the transition, the way new nations always have, and how Texans feel about being American is a separate matter that no treaty touches. On the legal side, the scare stories about losing status are far weaker than people assume, and the live FAQ on citizenship walks through why.

Why this question comes up at all

People ask this because they have been told independence means renouncing something they love. It does not. You are not required to trade away an identity to govern yourself. The choice to call yourself American, Texan, both, or something else stays exactly where it should: with you.

The bottom line

Texans could absolutely still consider themselves American if that is how they feel. Independence changes the government, not the person. Identity stays personal, and it stays yours.